Chapter 1: Q. 1.18 (page 16)

A committee of $7$ , consisting of $2$ Republicans, $2$ Democrats, and $3$ Independents, is to be chosen from a group of $5$ Republicans, $6$ Democrats, and $4$ Independents. How many committees are possible?

Short Answer

Expert verified

The possible number of committees are $600$ .

Step by step solution

Step 1. Given information.

Here it is given that,

Number of Republicans $= 7$

Number of Republicans to be selected $= 2$

Number of Democrats $= 6$

Number of Democrats to be selected $= 2$
Number of Independents $= 4$

Number of Independents to be selected $= 3$

Step 2. Find the possible number of committees.

Two Republicans can be selected in $(\begin{matrix} 5 \\ 2 \end{matrix})$ ways $= \frac{5!}{2! 3!} = \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!} = 10$

Two Democrats can be selected in $(\begin{matrix} 6 \\ 2 \end{matrix})$ ways $= \frac{6!}{2! 4!} = \frac{6 \times 5 \times 4!}{2 \times 1 \times 4!} = 15$

Three Independents can be selected in role="math" localid="1647788797198" $(\begin{matrix} 4 \\ 3 \end{matrix})$ ways $= \frac{4!}{3! 1!} = \frac{4 \times 3!}{3!} = 4$

Therefore, the the possible number of committees are $= 10 \times 15 \times 4 = 600$ .

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A committee of $7$ , consisting of $2$ Republicans, $2$ Democrats, and $3$ Independents, is to be chosen from a group of $5$ Republicans, $6$ Democrats, and $4$ Independents. How many committees are possible?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the possible number of committees.

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A committee of 7, consisting of 2 Republicans, 2 Democrats, and 3 Independents, is to be chosen from a group of 5 Republicans, 6 Democrats, and 4 Independents. How many committees are possible?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the possible number of committees.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

A committee of $7$ , consisting of $2$ Republicans, $2$ Democrats, and $3$ Independents, is to be chosen from a group of $5$ Republicans, $6$ Democrats, and $4$ Independents. How many committees are possible?