/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q5. Evaluate each expression.C(10,4)... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Evaluate each expression.

C(10,4)

Short Answer

Expert verified

210

Step by step solution

01

Step 1. Combination formula.

The number of combinations of nobjects taken rat a time is the quotient ofn! and (n−r)!r!, that is, C(n,r)=n!(n−r)!r!.

02

Step 2. Substitution.

Substitute 10 for nand 4 for rinto combination formula.

C(10,4)=10!(10−4)!4!

03

Step 3. Simplify.

Simplify the above obtained expression.

C(6,3)=10!6!4!=10â‹…9â‹…8â‹…7â‹…6â‹…5â‹…4â‹…3â‹…2â‹…16â‹…5â‹…4â‹…3â‹…2â‹…1â‹…4â‹…3â‹…2â‹…1=210

The solution of given expression is 210.

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