Chapter 1: Q. 1.16 (page 20)

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

Short Answer

Expert verified

The possible no. of subsets are $3480$ .

Step by step solution

Step 1. Given information.

The given set is $S = \{1, 2, . . ., 20\}$

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

Step 2. Find the number of subsets.

No. of ways to select $4$ numbers out of $20$ isrole="math" localid="1649164747337" $(\begin{matrix} 20 \\ 4 \end{matrix}) = \frac{20!}{4! 16!} = 4845$

The set of size $4$ must 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 $4$ numbers out of $15$ is role="math" localid="1649164852115" $(\begin{matrix} 15 \\ 4 \end{matrix}) = \frac{15!}{4! 11!} = 1365$

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the number of subsets.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Geometry

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

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

Step by step solution

Step 1. Given information.

Step 2. Find the number of subsets.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Geometry

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.

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