Show your solution for the following. You are planning a trip and A, B, C, D, E,

Question

Show your solution for the following.

You are planning a trip and A, B, C, D, E, and F wish to join you. However C and D do not get on well together, and neither do A and E. B does not mind going with either A or C, but would not go if both join.

a) How many ways can you take your friends with your friends on a trip if your budget is only good for four people including yourself?

b) What is the probability that C will be included as one of the three companions if F will be taken out from the choices?

Explanation / Answer

Total people including you are = 6 + 1 = 7

C and D do not get on well together therfore take one between this two ( take D )

A and E do not get on well together therfore take one between this two ( take E )

B does not mind going with either A or C, but would not go if both join (take B )

Therefore total coming people are = you + F + B + D + E

= 5 People

But we have  budget is only good for four people including yourself

therfore you want to take 3 people from this 4

Therfore use permutation for arrangments :

n = 4 !

r = 3 !

a) No. of ways can you take your friends = 4 ! / ( 4 - 3 ) !

= 24

b) Probability that C will be included as one of the three companions if F will be taken out from the choices.

Total people including you are = 5 + 1 = 6 ( F is not )

C and D do not get on well together therfore take one between this two ( take C )

A and E do not get on well together therfore take one between this two ( take E )

B does not mind going with either A or C, but would not go if both join (take B )

Therefore total coming people are = you + B + C + E

= 4 People

And you have the budget of 4 people with including you. and selected people is also 4 with including C and exclude D.

Total possible way using permutation = 4(P)4 = 24

Probability = 4(P)4 / 4(P)4

= 24/24

= 1

Probability that C will be included as one of the three companions if F will be taken out from the choices is one ( 1 ).

>>>>>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>>>>>

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