Please help me please

The senior class at a very small high school has 25 students. Officers need to be elected for four positions: President, Vice-Pr

kirill115 [55]

Answer:

(a) The total number of ways to select 4 officers from from 25 students is 12,650.

(b) The total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

Step-by-step explanation:

(a)

It is provided that there are a total of n = 25 students.

Officers need to be elected for four positions:

President, Vice-President, Secretary, and Treasurer.

k = 4

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

Compute the number of ways to select 4 students from from 25 as follows:

${25\choose 4}=\frac{25!}{4!(25-4)!}$

$=\frac{25!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22\times 21!}{4!\times 21!}\\\\=\frac{25\times 24\times 23\times 22}{4\times 3\times 2\times 1}\\\\=12650$

Thus, the total number of ways to select 4 officers from from 25 students is 12,650.

(b)

It is provided that of the 25 students, there are 13 girls and 12 boys in the class.

For the post of President and Treasurer only girls are selected.

For the post of Vice-President and Secretary only boys are selected.

Compute the number of ways to select 2 girls for the post of President and Treasurer as follows:

${13\choose 2}=\frac{13!}{2!(13-2)!}$

$=\frac{13!}{2!\times 11!}\\\\=\frac{13\times 12\times 11!}{2!\times 11!}\\\\=\frac{13\times 12}{ 2\times 1}\\\\=78$

Compute the number of ways to select 2 boys for the post of Vice-President and Secretary as follows:

${12\choose 2}=\frac{12!}{2!(12-2)!}$

$=\frac{12!}{2!\times 10!}\\\\=\frac{12\times 11\times 10!}{2!\times 10!}\\\\=\frac{12\times 11}{ 2\times 1}\\\\=66$

The number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is:

${13\choose 2}\times {12\choose 2}=78\times 66=5148$

Thus, the total number of ways the four officers are selected such that the President and Treasurer are girls and the Vice-President and Secretary are boys is 5,148.

7 0

2 years ago

The difference of two numbers.(a,b) is 21. The difference of 5 times a and 2 times b is 18. What are the values of a,b?

ziro4ka [17]

The equation is b-a= 21;
2b-5a = 18
a=8 and b= 29
therefore 29-8= 21
2 (29) -5 (8) = 18
58-40=18

7 0

3 years ago

The first house on the street has a lawn that is 300 feet long. The second house

Ivanshal [37]

Answer: 450

Step-by-step explanation:

first house--300

second house--50

third house--50 x2=100

300+50+100=450

5 0

3 years ago

Camryn earns $198.60 per week. She works 15 hours each week. How much does Camryn earn per hour? P.S this is a unit rate questio

Musya8 [376]

Okay, so in order to find how much she earns per hour you'll take the salary she earns each week ($198.60) and divide that to how many hours she works every week (15 hours). It'll look like: 198.60 / 15= $13.24 per hour.

4 0

2 years ago

In one poem, which "poor and country-bred" figure is said to have caused smart people to "laugh at him" and ask, "How can so ver

Kay [80]

Abraham Lincoln, i've read that story a long time ago myself and I remember who said that.

6 0

3 years ago