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Chapter 1: Q. 1.16 (page 20)

How many subsets of size 4of the set localid="1649163905451" role="math" S=1,2,...,20contain at least one of the elements 1,2,3,4,5?

Short Answer

Expert verified

The possible no. of subsets are3480.

Step by step solution

01

Step 1. Given information.

The given set isS=1,2,...,20

The object is to find the number of subsets of size 4which contains at least one of the elements 1,2,3,4,5.

02

Step 2. Find the number of subsets.

No. of ways to select 4numbers out of 20isrole="math" localid="1649164747337" 204=20!4!16!=4845

The set of size 4must contain at least one of the elements 1,2,3,4,5. So, the remaining numbers in set S will be 15.

No. of ways to select 4numbers out of 15is role="math" localid="1649164852115" 154=15!4!11!=1365

Therefore, the possible no. of subsets are=4845-1365=3480

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