In how many ways can you choose a group of four persons out of three girls and seven boys such that the group has only one girl?Choices:- 105 210 120 224

To solve this problem, we use the concept of combinations in probability.

Step 1: We need to select 1 girl out of 3. The number of ways to do this is given by the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of options, r is the number of options to choose, and '!' denotes factorial. So, C(3, 1) = 3! / [1!(3-1)!] = 3.

Step 2: We need to select 3 boys out of 7. Using the same formula, C(7, 3) = 7! / [3!(7-3)!] = 35.

Step 3: Since these are independent events, we multiply the results together. So, the total number of ways to choose a group of four persons such that the group has only one girl is 3 * 35 = 105.

So, the correct answer is 105.