From a group of 8 boys and 6 girls, in how many ways can a group of 5 be chosen so as to include at least one girl?Choices:- 240 1720 1840 1946

To solve this problem, we first need to understand that it involves combinations, which are ways of choosing items from a group without regard to the order of selection.

Step 1: Calculate the total number of ways to choose 5 people from a group of 14 (8 boys and 6 girls). This can be done using the combination formula nCr = n! / r!(n-r)!, where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

So, the total number of ways is 14C5 = 14! / 5!(14-5)! = 2002 ways.

Step 2: Calculate the number of ways to choose 5 boys from the group of 8 boys. This is done to later subtract this from the total number of ways, as we want at least one girl in the group.

So, the number of ways to choose 5 boys is 8C5 = 8! / 5!(8-5)! = 56 ways.

Step 3: Subtract the number of ways to choose 5 boys from the total number of ways to get the number of ways to choose a group of 5 that includes at least one girl.

So, the number of ways is 2002 - 56 = 1946 ways.

Therefore, the answer is 1946.