1-Looking at your trophy collection more closely, you note that you have three p

Question

1-Looking at your trophy collection more closely, you note that you have three ping-pong trophies, three volleyball trophies, and two math trophies. You decide to put them on the shelf in such a way that all the trophies of the same type are together. In how many ways can this be done?

2- After looking at the shelf for a while, you decide that it would look best if all the volleyball trophies came first, then the math trophies, and then the ping-pong trophies. In how many ways can this be done?




1-Looking at your trophy collection more closely, you note that you have three ping-pong trophies, three volleyball trophies, and two math trophies. You decide to put them on the shelf in such a way that all the trophies of the same type are together. In how many ways can this be done?

2- After looking at the shelf for a while, you decide that it would look best if all the volleyball trophies came first, then the math trophies, and then the ping-pong trophies. In how many ways can this be done?

Explanation / Answer

1. considering trophies of same type to be in a group..hence 3 groups

number of ways they can be arranged = 3! = 6 ways

now they can be rearranged among themselves

ping pontrophies can arrange between themselves=3!

volley = 3!

math =2!

total arrangements= 6*6*6*2=432 ways

2.

2!*3!*3!=72 ways

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