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1. Prove that C(n, r) = n!/r!(n – r)!

1. Prove that C(n, r) = n!/r!(n – r)!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Prove that C(n, r) = n!/r!(n – r)! 2. Between 10000 and 60000, find the number of even integers in which no digit is repeated. 3. There are 12 students in a party. Four of them are girls. In how many ways can these 12 students be arranged in a row if a) there are no restrictions; b) the 4 girls must be together (forming a block); c) no two girls are adjacent; d) between two particular boys A and B, there are no boys but exactly 3 girls.
Transcribed Image Text:1. Prove that C(n, r) = n!/r!(n – r)! 2. Between 10000 and 60000, find the number of even integers in which no digit is repeated. 3. There are 12 students in a party. Four of them are girls. In how many ways can these 12 students be arranged in a row if a) there are no restrictions; b) the 4 girls must be together (forming a block); c) no two girls are adjacent; d) between two particular boys A and B, there are no boys but exactly 3 girls.
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