"A Congressional cumittee of three is to be..." solved and explained

High School
Statistics and Probability
High school statistics
Data distributions

krypsojx

Answered question

2021-11-25

A Congressional cumittee of three is to be chosen from a set of five Democrats, three Republicans and four independents.
In how many ways can the committee be chosen, if it must have at least one Democrat and at least one Republican?

Answer & Explanation

Melinda Olson

Beginner2021-11-26Added 20 answers

Given:
Number of Democrat

= 5

Number of Republicans

= 3

Number of Independents

= 4

Step 2
Number of ways the committee be chosen, at least one Democrat and at least one Republican

= (^{{5}} C_{1} \times^{3} C_{1} \times^{4} C_{1}) + (^{{5}} C_{2} \times^{3} C_{1}) + (^{{5}} C_{1} \times^{3} C_{2})

= (5 \times 3 \times 4) + (10 \times 3) + (5 \times 3)

= 60 + 30 + 15

= 105

There are 105 ways the committee be chosen, at least one Democrat and at least one Republican

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