Hard counting problem (from Kaplan Qbank):

GRE Quant Problem Solving
1

Hey community! I was wondering if anyone could help me understand how to get to the answer here:

Capture
Capture1402×196 32.3 KB

2

There are 3 possible combinations of the number of alphabets or numbers in the code:

  1. 4 A + 2N:
    Total no. of possible combinations would be = 26 x 25 x 24 x 23 x 10 x 9
    All of these combinations of alphabets and numbers can be arranged in multiple ways:
    AAAANN, NNAAAA, NAAAAN, etc.
    The total number of such arrangements would be 6!/(4! x 2!) = 15
    Total unique access codes = 15 x 26 x 25 x 24 x 23 x 10 x 9

  2. 3A + 3N:
    Total no. of possible combinations would be = 26 x 26 x 24 x 10 x 9 x 8
    All of these combinations of alphabets and numbers can be arranged in multiple ways:
    AAANNN, NNNAAA, NNAAAN, etc.
    The total number of such arrangements would be 6!/(3! x 3!) = 20
    Total unique access codes = 20 x 26 x 25 x 24 x 10 x 9 x 8

  3. 2A + 4N:
    Total no. of possible combinations would be = 26 x 25 x 10 x 9 x 8 x 7
    All of these combinations of alphabets and numbers can be arranged in multiple ways:
    AANNNN, NNNNAA, NNAANN, etc.
    The total number of such arrangements would be 6!/(2! x 4!) = 15
    Total unique access codes = 15 x 26 x 25 x 10 x 9 x 8 x 7

Adding all of that up we have:
(26 x 25 x 10 x 9)(15 x 24 x 23 + 20 x 24 x 8 + 15 x 8 x 7)
(26 x 25 x 10 x 9 x 8 x 5)(3x3x23 + 4x24x1 + 3x1x7)
m(207 + 96 + 21)
324 m

3

This took me a good 10 minutes to solve

Can such questions come on GRE??

4

Nup

1 Like
5

Thanks @vidishas99 ! so helpful :slight_smile: .