**Problem**

Given two integers ‘N’ and ‘M’, representing the total number of boys and girls respectively, you have to find the number of ways to form a team of size ‘K’, containing at least 4 boys and at least 1 girl.

**Constraints: **

4 <= N <= 25

1 <= M <= 25

5 <= K <= N + M.

**Example - **

**Input:** N = 5, M = 3, K = 6

**Output: **18

**Explanation:**

The total size of the team is 6, which means we can either choose 4 boys and 2 girls or 5 boys and 1 girl.

- Number of ways to choose 4 boys out of 5 is
^{5}C_{4}= 5, and the number of ways to choose 2 girls out of 3 is^{3}C_{2}= 3. Therefore, the number of ways to form a team of 4 boys and 2 girls is 5 * 3 = 15. - Number of ways to choose 5 boys out of 5 is
^{5}C_{5}= 1, and the number of ways to choose 1 girl out of 3 is^{3}C_{1}= 3. Therefore, the number of ways to form a team of 5 boys and 1 girl is 1 * 3 = 3.

Therefore, the total number of ways to form a team of size 6 is 15 + 3 = 18.

**Input: **N = 6, M = 4, K = 7

**Output: **100

Also see, __Euclid GCD Algorithm__

**Approach**

**Prerequisite - **__Combinations__

For a fixed size K, let us say we can form a team (i, j) where ‘i’ denotes the number of boys, and ‘j’ denotes the number of girls in the team. The following are the constraints on (i, j):

- i + j = K
- 4 <= i <= N
- 1 <= j <= M

From the first equation, we get:

j = K - i

By substitutiog it in third equation, we get:

1 <= K - i <= M

Therefore, we need to form a team of size (i, K - i) if the following conditions hold:

- 4 <= i <= N
- 1<= K - i <= M

Now we can iterate over the ‘i’ to find the composition of the teams that we can form. We can calculate the number of teams to form a team of a particular composition (i, j) by -

^{N}C_{i} * ^{M}C_{j}

To calculate the number of ways to form a team, we can add the answer over all the valid i and j.