Find out the number of combinations and the number of From Permutations for 9 objects taken 7 at a time.Express your answer in simplest form

Question

asked Feb 9, 2023 201k views

1 Answer

Jausen Brett · Answer 1 · 2023-02-14T23:48:11+0000

The formula for Combination is,

$nCr=(n!)/(r!\left(n-r\right)!)$

Given

Therefore,

$^9C_7=(9!)/(7!\left(9-7\right)!)$

Simplify

$\begin{gathered} (9!)/(7!\left(9-7\right)!)=(9!)/(7!(2!))=(9*8*7!)/(7!2*1)=(9*8)/(2)=9*4=36 \\ \therefore^9C_7=36 \end{gathered}$

The formula for Permutation is,

$nPr=(n!)/(\left(n-r\right)!)$

Given:

Therefore,

$^9P_7=(9!)/(\left(9-7\right)!)$

Simplify

$\begin{gathered} (9!)/(\left(9-7\right)!)=(9!)/(2!)=(9*8*7*6*5*4*3*2!)/(2!)=9*8*7*6*5*4*3 \\ =181440 \\ \therefore^9P_7=181440 \end{gathered}$

Hence, there are 36 combinations and 181440 permutations.