Question

Protip: Wolframalpha uses ner(x, y) for our (3) Click here for an example. The wedding party consists of the bride, the groom and 8 other indistinguishable guests for a total of 10 people. The photographer wants to arrange 6 of these people in a row. a) If the bride must be in the picture, the number of ways to do this is b) If the bride but not the groom must be in the picture, the number of ways to do this is c) If the bride and groom must both be in the picture, the number of ways to do this is d) If neither the bride nor the groom can be in the picture, the number of ways to do this is e) If exactly one of the bride or groom is to be in the picture, the number of ways to do this is

Answer 1

a) If the bride must be in the picture, we have to choose 5 people from the remaining 9 guests. We can do this in 9 choose 5 ways, which is:

nCr(9, 5) = 126 ways

b) If the bride but not the groom must be in the picture, we have to choose 1 person from the groom and 5 people from the remaining 8 guests. We can do this in 8 choose 5 ways, which is:

nCr(8, 5) = 56 ways

c) If the bride and groom must both be in the picture, we have to choose 4 people from the remaining 8 guests. We can do this in 8 choose 4 ways, which is:

nCr(8, 4) = 70 ways

d) If neither the bride nor the groom can be in the picture, we have to choose 6 people from the remaining 8 guests. We can do this in 8 choose 6 ways, which is:

nCr(8, 6) = 28 ways

e) If exactly one of the bride or groom is to be in the picture, we can choose the bride and 5 people from the remaining 8 guests, or the groom and 5 people from the remaining 8 guests. The number of ways to do this is:

nCr(8, 5) + nCr(8, 5) = 2 * nCr(8, 5) = 2 * 56 = 112 ways

Therefore, the answers are:

a) 126 ways

b) 56 ways

c) 70 ways

d) 28 ways

e) 112 ways