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Chapter 1: Q. 1.15 (page 16)

A dance class consists of 22students, of which 10are women and 12 are men. If 5men and 5women are to be

chosen and then paired off, how many results are possible?

Short Answer

Expert verified

The possible results are23,950,080.

Step by step solution

01

Step 1. Given information.

Total number of students =22

No. of men =12

No. of women=10

02

Step 2. Find the number of possible results.

No. of ways of selecting 5men out of 12= 12!5!7!=12脳11脳10脳9脳8脳7!5脳4脳3脳2脳1脳7!=792

No. of ways of selecting 5men out of 10= 10!5!5!=10脳9脳8脳7脳6脳5!5脳4脳3脳2脳1脳5!=252

No. of ways that 5men and 5women can be paired off = 5!=5脳4脳3脳2脳1=120

Therefore, the total number of possible results are =792脳252脳120=23,950,080

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