How Many 7 Digit Phone Numbers Are There Where the Digits in Increasing Order?

Manager

Joined: 29 Jun 2018

Posts: 52

Localisation: India

GPA: 4

GMAT ToolKit User

How many 8 digit cellular phone telephone set numbers are there in which the digits do [#permalink] 01 August 2019, 06:16

00:00

Question Stats:

46% (01:29) correct 54% (02:03) amiss based on 24 Roger Huntington Sessions

Pelt Show timer Statistics

How many 8 digit cellular phone phone numbers are there in which the digits do not step-up from left-hand to right ?

A) 17!/(8!9!)
B) 15!/(8!9!)
C) 12!/(9!8!)
D) 17!/(6!8!)
E) 12!/(8!7!)

Source: Private tutor

_________________

DS Meeting place Moderator

Joined: 19 Oct 2018

Posts: 2064

Location: India

How many 8 figure cell phone numbers are there in which the digits do [#permalink] Updated on: 01 Aug 2019, 13:08

A bit tedious approach tho

⦁ There is only 1 way when telephone number starts with '0'; That is '00000000'
⦁ Numeral of ways when telephone set number starts with 1 = n=8 (11111111, 11111110...........10000000)
⦁ Number of ways when number starts with 2 = Σn= n*(n+1)/2= 8*9/2=36
⦁ Number of ways when phone number starts with 3 = Σn*(n+1)/2= 120
⦁ Come of ways when phone number starts with 4 = Σ Σn*(n+1)/2= 330

We can control the pattern on pascal triangle that is similar to our in a higher place calculation

Total phone numbers contingent= 1+8+36+120+330+792+1716+3432+6435+11440= 24310

LMP wrote:

How many an 8 digit cell phone numbers are there in which the digits suffice not increase from left to right ?

A) 17!/(8!9!)
B) 15!/(8!9!)
C) 12!/(9!8!)
D) 17!/(6!8!)
E) 12!/(8!7!)

Source: Private tutor

Attachments

1853_Pascals_Triangle2000px-Pascal's_Triangle_rows_0-16.svg.jpg [ 135.5 KiB | Viewed 2640 times ]

Originally posted past nick1816 on 01 Aug 2019, 12:32.
Last edited by nick1816 on 01 Aug 2019, 13:08, emended 1 clock in total.

GMAT Coach

Connected: 24 Jun 2008

Posts: 3641

How many 8 digit cell phone numbers racket are there in which the digits do [#permalink] 01 Aug 2019, 12:53

It's not clear what the doubtfulness means - you could interpret it in one of 2 ways:

- the question could be interrogative "how umteen earphone numbers can we give where the digits do not strictly increase from left to right?" As the question is worded, that's how I'd interpret its meaning. Then we'd be counting well-nig every phone number -- 89731224 for instance, does non purely increase from left to honourable, since it sometimes goes risen and sometimes goes thrown. The sole numbers we would not count are numbers like 12345689 and 23456789. Assuming we can use any digit anywhere (so the number can beginning with zero - the call into question really should tell you if there are any restrictions like that, because many people volition assume thither are), we'd then have 10 choices for each fingerbreadth, and 10^8 possible phone numbers in total, strictly increasing or not. We'd past motivation to exclude all of the strictly increasing call up numbers. Simply if we right pickax two numbers from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and erase them, we'll be left with a string of ogdoad digits in flaring order, and then there are 10C2 = (10)(9)/2! = 45 strictly increasing numbers, and 10^8 - 45 that are non strictly increasing.

- just the doubtfulness could make up asking "how many earpiece numbers butt we gain where each figure after the initiatory is either less than or equalise to the digit before IT?", or in other dustup, sound numbers game with digits that are "constantly non-maximizing". Then we'd embody counting numbers like 99987100 and 65433331, because from one digit to the next, these numbers never go in the lead - they either stay the same or go under. From the answer choices, this is manifestly the pregnant your tutor intends. You can use a 'partitions' method to answer questions like this (though if you'rhenium preparing for the GMAT, you might ask your tutor to show you even off one official problem where you need to purpose partitions to get an answer). You can likewise look at the problem therein way: if ABCDEFGH is a constantly non-increasing string of 8 digits 'tween 9 and 0, then A, B-1, C-2, D-3, E-4, F-5, G-6, H-7 would need to be a strictly decreasing string out of eight integers between 9 and -7 (and contrariwise - from each dwindling sequence like that, we can make over a unique phone number). So we just need to count how many stringently decreasing sequences we can make of eight integers 'tween 9 and -7 inclusive, so we just take to choose 8 integers from the 17 in that range , and the answer is 17C8 = 17! / (8!)(9!).

You South Korean won't need to do this kind of thing on the GMAT though.
_________________

GMAT Tutor in Montreal

If you are looking at for online GMAT math tutoring, or if you are fascinated in buying my advanced Quant books and problem sets, please meet me at ianstewartgmat at gmail.com

Manager

Coupled: 29 Dec 2018

Posts: 91

Location: India

WE:Marketing (Real Estate)

Rhenium: How many 8 digit cellular phone sound numbers are there in which the digits do [#permalink] 01 Aug 2019, 19:03

Take the above 2 solutions but nonetheless unclear how to become about in the echt test scenario

I would like to request moderators to throw much light on this chetan2u, Gladiator59, VeritasKarishma, Bunuel, generis, gmatbusters
_________________

Keep back your eyes on the prize: 750

Manager

Joined: 02 Jun 2014

Posts: 59

Location: India

Re: How umteen 8 finger's breadth cell earpiece numbers are there in which the digits manage [#permalink] 01 Aug 2019, 19:34

Need a proper OA and official explanation.

This seems way likewise problematical.

Pascals Triangle approach cant be due from to the highest degree of America and i cant entertain any other resolution.

Posted from my mobile device

Contemporary Student

Joined: 17 Jul 2018

Posts: 74

Localization: India

Denseness: Finance, Leaders

GMAT 1: 760 Q50 V44 Verified score

GPA: 4

Re: How many 8 digit cell headphone numbers racket are there in which the digits act [#permalink] 01 Aug 2019, 20:50

LMP wrote:

How many 8 digit cell phone numbers are there in which the digits do not increase from left to right ?

A) 17!/(8!9!)
B) 15!/(8!9!)
C) 12!/(9!8!)
D) 17!/(6!8!)
E) 12!/(8!7!)

Source: Private tutor

For solving the oppugn we need to understand two things:
1) Not in Ascending order doesn't mean in downward-arching gild. In 55444331 digits are not in ascending order but not of necessity in descending as comfortably for eg 55. another example, in number 88888888, the digits are not in rise order
2) This is not a switc but a combination question. Afterward we select the digits there is only combined possible combining in which the digits is not in ascendant order. 55444331 cant personify statute in any other way as per constraints of the doubt

Now approaching the question.
1) Eastern Samoa order doesn't matter, we just need to select digits for our number. Thus all figure spaces in the 8 digit number xxxxxxxx are of equal importance.
2) We motivation to select from among 10 numbers from 0-9, thence this question is basically asking us to divide the 8 digits xxxxxxxx into 10 spaces , the the right way most is for 9 and left most is for 0, and the number of x which falls in the range of a fingerbreadth (0-9) is the frequency of that digit in our final 8 digit amoun. An example would look like-minded this ||xx|xxx||xx|x||| is 77666443.

Archetypical line can be drawn in 9 slipway, second in 10 and 9th in 17 shipway and line can arrange amongst themselves in 9! ways. therefore the answer is 17!/9!8!. A.
Or using formula (n+r-1)C(r-1)=17!/8!9! A, where n is objects to be distributed (x) and r is number of boxes/ here digits (lines is r-1).

Please hit Kudos, if you liked the account.

Re: How many a 8 digit cellular telephone phone numbers are there in which the digits do [#permalink]

01 Aug 2019, 20:50

Moderators: