Using the combination formula, it is found that:
1. A. 7 combinations are possible.
B. 21 combinations are possible.
C. 1 combination is possible.
2. There are 245 ways to group them.
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Exercise 1, item a:
One letter from a set of 7, hence:
[tex]C_{7,1} = \frac{7!}{1!6!} = 7[/tex]
7 combinations are possible.
Item b:
Two letters from a set of 7, hence:
[tex]C_{7,2} = \frac{7!}{2!5!} = 21[/tex]
21 combinations are possible.
Item c:
7 letters from a set of 7, hence:
[tex]C_{7,7} = \frac{7!}{0!7!} = 1[/tex]
1 combination is possible.
Question 2:
Three singers are taken from a set of 7, and four dances from a set of 10, hence:
[tex]T = C_{7,3}C_{10,4} = \frac{7!}{3!4!} \times \frac{10!}{4!6!} = 245[/tex]
There are 245 ways to group them.
More can be learned about the combination formula at https://brainly.com/question/25821700
