Question

Hogwarts has 40 new transfer students - 12 in the Gryffindor house, 8 in the Hufflepuff house, and 20 in the Ravenclaw house. Which of the following is equal to the number of ways to line up for a picture 5 students from each house, Gryffindor on the left, Hufflepuff in the middle, Ravenclaw on the right? A. C(40/5) / 3 B. P(12,5) + P(8,5) + P(20,5) C. C(12,5) + C(8,5) + C(20,5) D. P(12,5) * P(8,5) * P(20,5) E. C(12,5) * C(8,5) * C(20,5)

Answer 1

To find Number of ways to line up for a picture - As order is important - Permutations is appropriate to use.

Number of students in Gryffindor house - 12

Number of students in Hufflepuff house - 8

Number of students in Ravenclaw house - 20

number of ways to line up for a picture 5 students from each house, Gryffindor on the left, Hufflepuff in the middle, Ravenclaw on the right

Number of ways to line up 5 students from Gryffindor on the left = P(12,5)

Number of ways to line up 5 students from Hufflepuff in the middle = P(8,5)

Number of ways to line up 5 students from Ravenclaw on the right = P(20,5)

number of ways to line up for a picture 5 students from each house, Gryffindor on the left, Hufflepuff in the middle, Ravenclaw on the right =

P(12,5) * P(8,5) * P(20,5)

Answer :

D. P(12,5) * P(8,5) * P(20,5)