Please show all work! thanks 3. A campus singing group, \"The Whole Notes\", wil

Question

Please show all work!

thanks

3. A campus singing group, "The Whole Notes", will have 12 members and is holding auditions. Suppose that there are 25 people auditioning to be in "The Whole Notes". Fifteen of those auditioning are women a) How many ways can the singing group be formed from among these 25 people? b) What is the probability that the singing group will be evenly split between men and women? c) What is the probability that at least 2 men will be in the singing group? d) What is the probability that the singing group will be all female? e) Suppose that the singing group, there will be 3 sopranos, 4 altos, 3 tenors, and 2 basses. Of the 25 people auditioning to be in the group, 9 are sopranos, 8 are altos, 6 are tenors and the rest are basses. How many ways are there to form "The Whole Notes"? All 25 singers are asked to take a written music theory test. The top 6 scorers will be ranked (regardless of vocal part). How many possible rankings of the top 6 are there from among all the singers? f)

Explanation / Answer

(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)

a) There are 25 people and 12 need to be selected.

This can be done in 25C12 ways.

b) Of the 25, 15 are women and 10 are men.

The number of ways 6 men are selected out of 10 = 10C6

The number of ways 6 women are selected out of 15 = 15C6

=> Probability that same (6) number of men and women are chosen

= 10C6 * 15C6 / 25C12

Let us calculate d) before c)

d) The number of ways to select 12 women out of 15 = 25C12

=> Probability that all are women in the singing group

= 15C12 / 25C12

c) Now let us calculate the probability that there is only one man in the singing group

The number of ways to select 1 man out of 10 = 10

The number of ways to select 11 women out of 15 = 15C11

=> Probability that there is only one man in the group

= 10 * 15C11 / 25C12

=> Probability that there is atmost one man in the group (using the result of d))

= 15C12 / 25C12 + 10 * 15C11 / 25C12

=> Probability that there are atleast two men in the group

= 1 - (15C12 / 25C12 + 10 * 15C11 / 25C12)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.