Question

Determine the number of possible combinations in a state lottery where 7 numbers must be selected from a given set of numbers. answer parts​ a) through​ e) below. question content area bottom part 1 ​a) 7 of 51 numbers there are enter your response here possible combinations. ​(simplify your answer. type an integer or a​ fraction.)from the 6 male and 11 female sales representatives for an insurance​ company, a team of 3 men and 4 women will be selected to attend a national conference on insurance fraud.

in how many ways can the team of 7 be​ selected?

Answer 1

There are
`\( \binom{6}{3} * \binom{11}{4} \)`ways to select a team of 3 men and 4 women from 6 male and 11 female representatives, totaling to 440 possible combinations.

Explanation:

The problem involves selecting a team consisting of 3 men and 4 women from a pool of 6 male and 11 female representatives, respectively. The number of ways to choose 3 men out of 6 is represented by
`\( \binom{6}{3} \),`which equals 20. Simultaneously, the ways to select 4 women out of 11 is denoted by
`\( \binom{11}{4} \),` equating to 330. To determine the total number of possible combinations, these individual selections need to be multiplied together, resulting in
`\( \binom{6}{3} * \binom{11}{4} = 20 * 330 = 440 \)`ways to form a team with the specified gender composition.

This approach leverages the concept of combinations from the given sets of male and female representatives, ensuring the selection of 3 men and 4 women for the insurance conference team.