Combinations and Permutations

Hi everyone!

Looking for someone to check over the work I have done so far to see if im on the right track. Also looking for some help to start the questions I am really stuck on.

Thank you!

1.) P(12,5)

For this one, would I just use the *n*P*r* button on my calculator to get the answer of 95040?

2.) ( 7 ) + ( 8 )

( 3 ) ( 3 )

The above brackets ^^ are meant to be continuous.

I am not sure how to solve this. The instructions just say to Evaluate each expression and this is review for me so I cant quite remember how to start.

3.) What is the seventh term in the expansion of (3 - 2x)^15 ?

Using the formula tk+1= nCk (x)^n-k(y)^k

n=15

x=3

y=-2x

k= one less than the term you want. Since I am looking for the seventh term k would be 6.

t6+1=15C6(3)^15-6 (-2x)^6

t7=5005(3)^9 (-2x)^6

t7=5005(19683) (-64x^6)

t7= -6,304,858,560x^6

This number seems extremely large to be the correct answer.

4.)a.) *P*(*n,*2)+ *P*(*n*,3)= 42(*n-*1)

*b.) C*(*n*,2) + *C*(*n*,1)= *C*(7,2)

Not sure how to start either of these questions as this is review and I learned these types of problems months ago.

5.) Last month 200 students enrolled in courses: 56 students took English; 52 took mathematics; 72 took history; 12 took mathematics and English; 19 took mathematics and history; 18 took English and history; and 7 took all 3 courses.

a.) How many students took English or mathematics or history?

b.) How many students did not take English, mathematics, or history?

Any help with any of these questions and reviews of the ones I have already done would be GREATLY appreciated.

Thanks!