Frank, Grey, Hala, and Inez will ride in the same car on the field trip. Three of the children will sit in the back seat of the car. What are the 4 possible combinations of three children? Use the abbreviations F, G, H, and I in your list. (Hint: The order of the children does not matter.)

(FGH ; FGI ; GHI ; HIF)

Step-by-step explanation:

Frank, = F

Grey = G

Hala = H

Inez = I

3 children sitting in the back seat :

Using combination formula :

4C3

nCr = n! /(n-r)! r!

4C3 = 4! / 1! 3!

4C3 = 4 / 1 = 4

The 4 Possible combinations are :

(FGH ; FGI ; GHI ; HIF)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: