Question

Four of the letters of the word PAINTBRUSH are selected at random. Find the number of different combinations if

a) there is no restriction on the letters selected
b) the letter T must be selected.​

Answer 1

504 combinations.
In a combination, the elements of a subset can be written in any order.
There are 9 letters on the word paintbrush, excluding the letter T.
Since the letter T must be included in all subsets, there are 3 spots left to fill.
To fill the first spot, you could pick from any of 9 letters.
To fill the second spot, you could pick from any of 8 letters, excluding the one in the first slot.
To fill the third slot, you could pick from any of. 7 previously unpicked letters. This can be expressed a 9*8*7, which equals 504.