Question

find the indicated probability.
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)

0.06268

0.07776

0.09537

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

Step3: Calculate probability

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

Answer:

\(0.00533\)