Question

a charity is conducting a raffle, and it sells one ticket each to 35 women and 21 men. if 5 winners are randomly selected, what is the probability that they are all men? round to five decimal places. (1 point) 0 0.06268 0 0.07776 0 0.09537 0 0.00533

Explanation:

Step1: Calculate total number of tickets

Total number of tickets \(n = 35+21=56\)

Step2: Use combination formula

The number of ways to choose \(5\) men out of \(21\) is \(C(21,5)=\frac{21!}{5!(21 - 5)!}=\frac{21!}{5!×16!}=\frac{21\times20\times19\times18\times17}{5\times4\times3\times2\times1}=20349\)
The number of ways to choose \(5\) tickets out of \(56\) is \(C(56,5)=\frac{56!}{5!(56 - 5)!}=\frac{56!}{5!×51!}=\frac{56\times55\times54\times53\times52}{5\times4\times3\times2\times1}=3819816\)

Step3: Calculate probability

Probability \(P=\frac{C(21,5)}{C(56,5)}=\frac{20349}{3819816}\approx0.00533\)

Answer:

\(0.00533\)