Question

for these problems state whether it is. permutation or combination and find the number of possibilities.

1) There are 35 people at a luncheon. They each shake hands with everyone else. How many handshakes were there? 30C2 35 15,34,43,423,7 order doesn't matter: Combination -26, 1572 2' (35-2).

Answer 1

1)

35 people at luncheon. They each shake hands with everyone else.

Number of handshakes $\frac{(n)(n-1)}{2}$

$\frac{(n)(n-1)}{2} = \frac{35*34}{2}= 595$

595 handshakes.

2)

$_{12}C_{3}= \frac{12!}{3! * 9!} = \frac{12*11*10*9!}{3*2*1! * 9!}= \frac{12*11*10}{3*2*1}=220$

3)

$_{17}C_{3}= \frac{17!}{3! * 14!} = \frac{17*16*15*14!}{3*2*1! * 14!}= \frac{17*16*15}{3*2*1}=680$

4)

$_{14}P_{4}= \frac{14!}{(14-4)!} = \frac{14*13*12*11*10!}{10!}= 14*13*12*11=24024$