VeritasPrepKarishma wrote:

ravisinghal wrote:

two letters should be identical :-

first letter can be chosen in 26 ways

second in 1 way

num of ways to arrange these :- 26/2! =13

two numbers to be even : -

one has to be from 0,2,4,6,8 = 5 ways

second can be any 1 from the 10 digits = 10 ways

total ways :- 13 * 5 *10 =650...answer B

A few things to think about:

- Once you have chosen a letter in 26 ways, there is only 1 way of arranging them. e.g. if you have chosen C, there is only one way of arranging CC.

- To get an even product, it is possible that the first digit is odd and the second one is even.

Responding to a pm:

Then how do you please explain questions like arranging Mississippi etc..where identical objects to be divided...

similar case with CC also..??

Ways of arranging ABC = 3!

ABC

ACB

BAC

BCA

CAB

CBA

Ways of arranging AABC = 4!/2!

Assume the two As are different - \(A_1\) and \(A_2\). Ways of arranging = 4!

But the two As are the same. So \(A_1BCA_2\) is the same as \(A_2BCA_1\) etc. So divide by 2.

By the same logic:

Ways of arranging CC = 2!/2! = 1

_________________

Karishma

Veritas Prep GMAT Instructor

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