Question

Evaluate 10c4 and 11p5

Answer 1

To evaluate permutations and combinations, we use the following formulas:

`\begin{gathered} nPr=(n!)/((n-r)!) \\ \\ nCr=(n!)/(r!(n-r)!) \end{gathered}`

where n is the total number of objects and r is the number of objects selected from the set.

Following the formulas above, we can solve 10C4 and 11P5.

`\begin{gathered} 10C4=(10!)/(4!(10-4)!) \\ \\ 10C4=\frac{10!}{4!\text{ }6!} \\ \\ 10C4=(10\cdot9\cdot8\cdot7\cdot6!)/(4\cdot3\cdot2\cdot1\cdot6!) \\ \\ 10C4=10\cdot3\cdot7 \\ \\ 10C4=210 \end{gathered}`
`\begin{gathered} 11P5=(11!)/((11-5)!) \\ \\ 11P5=(11!)/(6!) \\ \\ 11P5=(11\cdot10\cdot9\cdot8\cdot7\cdot6!)/(6!) \\ \\ 11P5=11\cdot10\cdot9\cdot8\cdot7 \\ \\ 11P5=55,440 \end{gathered}`

The answers are 210 and 55,440.