probability with permutation and combination

Question

Sylvester is in a music competition with 10 other musicians. The order of the performances is determined by drawing slips of paper from a bag. Event C: Sylvester is chosen to be last, and his two best friends are chosen to be first and second.

Answer 1

Three positions are to be considered as pre-set, or fixed, in Event C, so there are 7 other musicians who might be arranged in any order for the remaining positions.

 

P(C) = ₇P₇ ÷ ₁₀P₇