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Chapter 12: Q6. (page 797)

Evaluate each expression.

C(7,2)

Short Answer

Expert verified

21

Step by step solution

01

Step 1. Combination formula.

The number of combinations ofn objects takenr at a time is the quotient ofn! and (n鈭�r)!r!, that is, C(n,r)=n!(n鈭�r)!r!.

02

Step 2. Substitution.

Substitute 7 for nand 2 forr into combination formula.

C(7,2)=7!(7鈭�2)!2!

03

Step 3. Simplify.

Simplify the above obtained expression.

C(7,2)=7!5!2!=7鈰�6鈰�5鈰�4鈰�3鈰�2鈰�15鈰�4鈰�3鈰�2鈰�1鈰�2鈰�1=21

The solution of given expression is 21.

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