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22 Feb 2021, 05:15
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If m denotes the number of positive five-digit numbers whose digits are in strictly descending order, and n denotes the number of five-digit positive numbers whose digits are in strictly ascending order, what is the value of m - n?
(A) 10C4
(B) 9C5
(C) 10C3
(D) 9C3
(E) 9C2
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 10C4
(B) 9C5
(C) 10C3
(D) 9C3
(E) 9C2
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
If m denotes the number of 5 digit numbers of each successive digits are in their descending order magnitude and n is the corresponding figure, when the digits are in their ascending order of magnitude then (m – n) has the value
22 Feb 2021, 08:49
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Bunuel
We are basically choosing 5 digits where order is not important as each selection can have only one way in order.
For example : If you choose 1,7,3,9,5, then there is only one way in ascending order - 1,3,5,7,9
Each selection in descending order will have an ascending order except when 0 is also selected. Because 0abcd will make it a 4-digit number.
Therefore, m-n will be the selection where 0 is also there.
The ways when 0 is already there = ways to select 4 out of remaining 9 digits =9C4=\(\frac{9!}{(9-4)!4!}=\frac{9!}{5!(9-5)!}=9C5\)
B
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25 Jul 2026, 03:46
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where is the 'figure' mentioned in the question Bunuel
