Final answer:
To invite exactly 3 girls out of the 5 girl friends, the man can do so in 10 different ways. The correct answer is (b) (5/3)×(4/3).
Step-by-step explanation:
The student is asking for the number of ways to invite exactly 3 girls from a group of 5 girls and an unspecified number of boys. This is a problem of combinations where we are looking to choose a subset without regard to the order of selection. Since the question is only about choosing girls, we can ignore the boys for now.
To find the number of ways to invite exactly 3 girls, we use the combination formula which is:
C(n, k) = n! / [k! * (n - k)!],
To find the number of ways the man can invite exactly 3 girls out of his 5 girl friends, we can use the combination formula. The formula for combinations is nCr = n! / (r! * (n-r)!). In this case, n = 5 (number of girls) and r = 3 (number of girls to be invited).
Plugging in the values, we get 5C3 = 5! / (3! * (5-3)!) which simplifies to 10.
Therefore, the man can invite his friends in 10 different ways if he wants exactly 3 girls to be part of the invitee.