How many ways a 6 member team can be formed having 3 men and 3 ladies from a group of 6 men and 7 ladies? Options : 700 720 120 500
Question
How many ways a 6 member team can be formed having 3 men and 3 ladies from a group of 6 men and 7 ladies?
Options : 700 720 120 500
Solution
The solution to this problem involves using combinations.
Step 1: We need to select 3 men out of 6. The number of ways to do this is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of options, r is the number of options to choose, and '!' denotes factorial. So, C(6, 3) = 6! / [(6-3)!3!] = 20.
Step 2: We need to select 3 ladies out of 7. Using the same formula, C(7, 3) = 7! / [(7-3)!3!] = 35.
Step 3: Since these are independent events, we multiply the results together to get the total number of ways to form the team. So, 20 * 35 = 700.
So, the answer is 700.
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