Answer:
4. She can dress them up in 6,720 ways
Explanation:
P = 8!/(8-5)!= 8!/3!=6,720 ways
5. Answer: There are 48 ways of sitting 6 people in a table with two of them insisting to be sitting beside each other.
Explanation:
There are 6 people and 2 need to be together. We can make the 2 count as 1 unit, and deal with it later. The problem temporarily becomes sitting 5 people on a round table.
To solve this we need to use the formula for circular permutation. The formula for circular permutation is given by where n is the number of objects. In this case, n = 5. Substituting to the formula, we get
(5 - 1)! = 4!
4 x 3 x 2 = 24
However, we know that one of the units counts for the other 2 that insist on sitting together. They can arrange themselves in 2! = 2 ways (person one, person two; or person two, then person one)
We multiply this to the number of ways 5 people can be sit in a table; because of fundamental principles of counting. Imagine that for those 24, person one comes first, we haven't counted the times where person two comes before person one. Person two coming first before person one still counts because person one and person two are still sitting beside each other.
