Answered: A planning committee for a major…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A planning committee for a major development project must consist six members. There are eight architects and five engineers to choose from.

In how many ways can a planning committee be chosen with at least three engineers( rounded of to zero decimals)? There is at least one architect and one engineer on the planning committee

Expert Solution

Step 1

There are 6 seats and a total of 13 members, 8 architects and 5 engineers.

Part 1: At least 3 engineers get selected

(i) 3 engineers from 5 can go to 3 seats in ⁵C₃ = $\frac{5!}{3! 2!}$ = 10 ways

and 3 architects from 8 can go to remaining 3 seats in ⁸C₃ = $\frac{8!}{3! 5!}$ = 56 ways

which gives $10 \times 56 = 560$ ways

(ii) 4 engineers from 5 can go to 4 seats in ⁵C₄ = $\frac{5!}{4! 1!}$ = 5 ways

and 2 architects from 8 can go to remaining 2 seats in ⁸C₂ = $\frac{8!}{2! 6!}$ = 28 ways

which gives $5 \times 28 = 140$ ways

(iii) 5 engineers from 5 can go to 5 seats in ⁵C₅ = $\frac{5!}{5! 0!}$ = 1 ways

and 1 architects from 8 can go to remaining 1 seats in ⁸C₁ = $\frac{8!}{1! 7!}$ = 8 ways

which gives $1 \times 8 = 8$ ways

Therefore, total number of ways in which at least 3 engineers will be chosen = 560 + 140+ 8 = 708 ways

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