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If m denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and n is the corresponding figure, when the digits are in their ascending order of magnitude, then ( m-n) has the value: (A) 10 C 4 (B) 9 C 5 (C) 10 C 3 (D) 9 C 3

If m denotes the number of 5 digit numbers if each successive digits are in their descending order of magnitude and n is the corresponding figure, when the digits are in their ascending order of magnitude, then (m-n) has the value:
(A) 10C4
(B) 9C5
(C) 10C3
(D) 9C3

Grade:11

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
Hi,

The answer is 9C4.
For descending order : to form a five digit no we need to choose 5 nos out of 10 nos, which is 10C5. Now u dont need to arrange them, there is only one way by which 5 different nos can be arranged in only one way.
But for ascending order we have only 9 options to choose from, as including 0 and arranging it in ascending order will put on the front and with zero on front the no will be a 4 digit no and not 5 (For ex : if you choose 0, 1, 2, 3, 4 the ascending order will be 01234 but this is a four digit no and not 5) So for this case we have 9C4 cases.

So m-n gives, 10C5-9C5 = 9C4.

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