Question

Determine if the problem is a combination or permutation and then find the answer.
How many different ways can the letters in MUSIC be arranged?

Answer 1

It will be a permutation because if it were a combination, the order would not matter. So it would be pointless if usmic were considered the same as cisum. So we have a permutation of 5 items taken 5 at a time. The formula for a permutation is \[(n!)/(n-k)!\] Where n is the total and k is the amount taken at a time. This gives us\[5!/(5-5)!\]By definition, 0! is 1 (Rather counter-intuitive I would say) so the denominator goes to 1 which leaves us with \[5!=120\] So there are 120 different ways to arrange the five letters in MUSIC.