Final answer:
For the given age groups and the number of individuals, there are 6 ways to select from the 21-30 age group, 15 ways from the 31-40 age group, and 20 ways from the 41-50 age group, resulting in 1800 possible committees.
Step-by-step explanation:
To determine how many ways a committee of 12 can be chosen given certain age restrictions and number of people available, we can use the concept of combinations. We are asked to form a committee of 12 where 5 members must be from the 21-30 age group, 4 must be from the 31-40 age group, and 3 from the 41-50 age group, with 6 available candidates in each group.
To select 5 members from the 6 available in the 21-30 age group, we can calculate the number of combinations by using the combination formula C(n, k) = n! / (k!(n-k)!) where 'n' is the number of items to choose from, and 'k' the number of items to select. Here, n=6 and k=5, so the formula gives us C(6, 5) = 6!/ (5!*(6-5)!) = 6 ways.
Similarly, to select 4 members from the 6 available in the 31-40 age group, we have C(6, 4) = 6! / (4!*(6-4)!) = 15 ways. And to select 3 members from the 6 available in the 41-50 age group, we have C(6, 3) = 6! / (3!*(6-3)!) = 20 ways.
As these selections are independent of one another, to find the total number of ways to create the committee, we multiply the number of ways for each independent selection. Thus, the total number of ways is 6 * 15 * 20 = 1800 ways.