can u please solve c and d? 8. [16 points] Brandon and Maria are on an eight-mem

Question

can u please solve c and d? 8. [16 points] Brandon and Maria are on an eight-member board of directors. (a) Suppose three members are to be selected to serve as President, Secretary, and Treasurer How many ways can the positions be assigned if Brandon and Maria cannot both be assigned? (b) Suppose three of the eight members are to be assigned to a planning committee. How many ways can they be assigned if neither Brandon nor Maria can be on the planning committee? ) 6. .120 (c) How many ways can three people be assigned to the planning committee if either Brandon or Maria, but not both, must be on the planning committee? (d) Suppose three of the eight members are to be selected to serve as President, Secretary, and Treasurer and three members from the remaining five are to be assigned to the planning committee. How many ways can all the positions be filled if there are no restrictions on Brandon's and Maria's positions? (20 (-)-1347 . to , 13, ywo 2

Explanation / Answer

I will solve all

Question 8

There are 8 member committee where Brandon and Maria are also included in the Committee.

(a) Brandon and Maria cannot be assigned so total number of ways = 6 * 5 * 4 = 120

(b) there are three members to be selected for planning committee so

number of ways to select by excluding Maria and Brandon = 6C3  = 20

(c) There must be atleast one should be in planning committe. That means first we will find the total number of possibites

Total possibilties without considering Brandon and Maria = 8C3 = 56

Number of possibilities when both are in committee = 6C1  = 6

Number of possibilites when both are not in committee = 6C3 = 20

So total possibilities that only one is in committee = 56 - 6 - 20 = 30

(d) Number of ways to seelct president = 8

for vice president = 7

for treasurer = 6

for plannig committee members = 5C3 = 10

so total number of possibilites = 8 * 7 * 6 * 10 = 3360

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