Question

Solve for r. This is for combinations and permutations.

Answer 1

○ D) A and C

Step-by-step Step-by-step explanation:

`\displaystyle (n!)/(r![-r + n]!) = {}_nC_r`

All you need to do is plug each choice into the formula:

`\displaystyle (10!)/(2![-2 + 10]!) \Longrightarrow ([2][3][4][5][6][7][8][9][10])/(2[-2 + 10]!) \longrightarrow ([2][3][4][5][6][7][8][9][10])/(2[(2)(3)(4)(5)(6)(7)(8)]) \\ \\ \boxed{45} = (90)/(2)`

OR

`\displaystyle (10!)/(8![-8 + 10]!) \Longrightarrow ([2][3][4][5][6][7][8][9][10])/([(2)(3)(4)(5)(6)(7)(8)][-8 + 10]!) \\ \\ \boxed{45} = (90)/(2)`

So, from what you see, both values of
`\displaystyle r` work. In fact, when using the formula pertaining to combinations, you will see that each result has a “repetitive pattern”. This is something you must look out for when using this formula.

I am joyous to assist you at any time.