1. Given S = {x│x is a distinct letter of the word “prism”}. How many valid events of the sample space S can be formed if it contains “s” but does not contain “m”?

Question

Please help.

Answer 1

We can eliminate “m”, and we are left with “s” and its permutations with “p”, “r” and “i”. This gives us:

s; sp, sr, si, ps, rs, is; spr, spi, sir, and all the permutations of these; spri and all its permutations.

There are 6 each of the 3-letter permutations.

When we add all these together we get: 1+6+3×6+24=1+6+18+24=49.