Answer
a. $1.3\times10^{-8}$
b. $3.27\times10^{-6}$
c. $4.17\times10^{-8}$
Work Step by Step
Total number of permutations 5 out of 52: $_{52}P_5$
a. Royal flush
Only 4 choices, $p=\frac{4}{_{52}P_5}$=$1.3\times10^{-8}$
b. Straight flush excluding Royal flush
Choices $4^5-4=1020$, $p=\frac{1020}{_{52}P_5}$=$3.27\times10^{-6}$
c. Four of a kind
Only 13 choices, $p=\frac{13}{_{52}P_5}$=$4.17\times10^{-8}$
