Question

Six numbered minions were waiting to be hired. 8 different Super Villains showed up.

a.) How many different ways can these minions be distributed? How many if they are each taken by a different villain?

b.) How many ways can they be taken with at least 2 taken by Gru?

c.) How many ways can they be taken with with 3 taken by 1 villain and 2 taken by another villain?

d.) How many ways can 2 minions be taken by each of 3 different villains?

e.) If the numbers of the minions are erased (so that they all look the same), how many ways can they be distributed?

Answer 1

We would be looking at the first 4 parts here as:

a) Number of different ways such that the minions can be distributed is computed here as:
= Number of villains * Number of villains * Number of villains ....... 6 times

= 8⁶

Therefore 8⁶ is the total number of ways that the minions could be distributed here.

Number of ways such that each is to be taken by a different villain is computed here as:

= Number of permutation of 8 items taken 6 at a time

b) Number of ways to distribute 6 minions such that there are at least 2 minions taken by Gru

= Total number of ways to distribute - Total number of ways in which Gru gets 0 or 1 minion

c) Number of ways to distribute the minions such that 3 of them are taken by 1 villain and 2 taken by another villain and therefore the last one taken by the third villain

= Number of ways to select 3 out of the 6 minions * Number of ways to select 1 villain from 8 villains * Number of ways to select 2 minions from the 3 minions left * Number of ways to select second villain from the remaining 7 villains * Number of ways to select the last villain from the remaining 6 villains

d) Number of ways that 2 minions be taken by each of 3 different villains is computed here as:

= Number of ways to select 3 villains from 8 villains * Number of ways to select 2 minions from 6 minions * Number of ways to select the 2 minions from remaining 4 minions