We are given that there are 8 men and 5 women in a panel, and we are asked to find the number of ways to form a committee of 3 women and 5 men.
The number of ways to choose 3 women from 5 women can be calculated using the combination formula:
\(C(n, r) = \frac{n!}{r!(n-r)!}\)
Where \(n\) is the total number of items, and \(r\) is the number of items to choose.
For choosing 3 women from 5, we have:
\(C(5, 3) = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10\)
Next, the number of ways to choose 5 men from 8 men is:
\(C(8, 5) = \frac{8!}{5!(8-5)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56\)
Now, to form the committee, we multiply the two values together:
\(10 \times 56 = 560\)
The number of ways to form the committee is 560.
How many possible words can be created from the letters R, A, N, D (with repetition)?