Chapter 13.9, Problem 21PPS

To determine

To Find: Given situation is permutation or combination.

Answer to Problem 21PPS

The number of ways is $2$ , as the handshakes is in pair and number of distinct handshake is $66$ .

Explanation of Solution

Given information:

  $12$ no. of people attending shakes hand with every other person exactly once.

Calculation:

The number of combinations,

  $=\frac{Thenumberofpermutations}{Thenumberofways}$

There are $12$ choices for the first person and $11$ choices for the rest.

Thus, the number of permutation is,

  $\begin{array}{l}P\left(12,2\right)=12\times 11\\ =132\end{array}$

Thus, the number of ways is $2$ , as the handshake is in pair.

Therefore, the number of combinations,

  $\begin{array}{l}=\frac{132}{2}\\ =66\end{array}$

The number of district handshake is $66$ .