A comedian knows five jokes. One joke is old, one joke is new, and the other jokes are somewhere between. If the order in which these jokes are told makes a difference in terms of how they are received, how many ways can they be delivered if the old joke is told first and the new joke is told last?

Question

A comedian knows five jokes. One joke is old, one joke is new, and the other jokes are somewhere between. If the order in which these jokes are told makes a difference in terms of how they are received, how many ways can they be delivered if the old joke is told first and the new joke is told last?

Answer 1

To determine the number of ways the remaining jokes can be delivered between the old joke and the new joke, we need to consider the number of arrangements.

There are 3 jokes remaining (excluding the old joke and the new joke), and we need to determine the number of ways these 3 jokes can be arranged. This can be done using the concept of permutations.

We have 3 options for the first joke, 2 options for the second joke, and 1 option for the third joke. Therefore, by the multiplication principle, the total number of arrangements is: 3 × 2 × 1 = 6.

However, we also need to consider the order of the old joke and the new joke. Since the old joke must be told first and the new joke must be told last, there is only one way to arrange them.

Therefore, the total number of ways the jokes can be delivered is: 6 × 1 = 6 ways.