Out of 7 gents and 4 ladies a committee of 5 is to be formed. The number of committees suchthat each committee includes at least one lady is

To find the number of committees that include at least one lady, we can use the concept of combinations.

First, let's consider the total number of committees that can be formed without any restrictions. We have a total of 11 people (7 gents and 4 ladies) to choose from, and we need to form a committee of 5.

The number of ways to choose 5 people out of 11 can be calculated using the combination formula, which is denoted as C(n, r) and is equal to n! / (r! * (n-r)!), where n is the total number of items and r is the number of items to be chosen.

Using this formula, we can calculate the total number of committees without any restrictions as C(11, 5) = 11! / (5! * (11-5)!) = 462.

Now, let's consider the number of committees that do not include any ladies. In this case, we only have the 7 gents to choose from, and we need to form a committee of 5. Using the same combination formula, we can calculate this as C(7, 5) = 7! / (5! * (7-5)!) = 21.

To find the number of committees that include at least one lady, we subtract the number of committees without any ladies from the total number of committees. Therefore, the number of committees that include at least one lady is 462 - 21 = 441.