There are 7 candidates for 3 seats, in how many ways the post be filled?

To find the number of ways the 3 seats can be filled with 7 candidates, we can use the concept of combinations.

The number of ways to choose 3 candidates out of 7 can be calculated using the formula for combinations, which is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of candidates and r is the number of seats available.

In this case, we have n = 7 (7 candidates) and r = 3 (3 seats). Plugging these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

Simplifying this expression, we have:

C(7, 3) = 7! / (3! * 4!)

Now, let's calculate the factorials:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 3! = 3 * 2 * 1 = 6 4! = 4 * 3 * 2 * 1 = 24

Substituting these values back into the formula, we have:

C(7, 3) = 5040 / (6 * 24)

Simplifying further:

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, there are 35 different ways the 3 seats can be filled with 7 candidates.