Question

I need help with 21 22 and 23

Answer 1

Hope this helps :)

Answers:

This can be found by using the combinations and permutations formulas.

Combinations being the C equation and Permutations being the P equation.

21:
`C_(6)(21) = \left[\begin{array}{ccc}21\\6\end{array}\right] =(21!)/(6!(21-6)!)=(21*20*19*18*17*16)/(6*5*4*3*2*1) = 54264`

answer: 54264

22:
`C_(2)(n) = \left[\begin{array}{ccc}n\\2\end{array}\right] =(n!)/(2!(n-2)!)= answer`

answers:

Art: 15

Writing: 21

Technology: 28

23:
`P(n,r)=(6!)/((6-6)!)=720`

answer: 720

Step-by-step explanation:

A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.