Question

In a group of 20 people, each person has to shake hands with each of the other persons in the group. Assuming that only 2 people can shake hands at one time:

a) How many different handshakes will there be?
b) Assuming it takes three seconds for each hand shake, how many minutes will it take for all of the handshakes to take place?

Answer 1

a) is the number of combinations of 2 in 20

if n = number of people and r = 2

nCr = n!
------
(n-r)! r!

n! = n factorial

eg 4! = 4*3*2*1 , 5! = 5*4*3*2*1

Answer 2

* n = total number, r = number in combination (in the above case this is 2)

Answer 3

are you familiar with this?

Answer 4

I used my calculator and got 190. Is this correct?
I learned using a calculator never done it by hand.

Answer 5

a quick way to do this is

20*19
------ = 380/2 = 190
2 * 1

yes right

Answer 6

I need more help with part "b"

Answer 7

thats 190 * 3 seconds
then divide by 60 to give time in minutes

Answer 8

9 and a half minutes?

Answer 9

yup

Answer 10

I have another problem I need help with see if you can figure this one out.


2. Five men and five women line up at a checkout counter in a store. In how many ways can they line up if the first person in line is a woman, and the people in line alternate woman, man, woman, man, and so on?

Answer 11

number of arrangements women can line up = 5!
.. .. .. .... .. men ..... .. = 5!

for each combination of women there is 5! of men

so total ways = 5! * 5!

Answer 12

You are a genius! Thanks so much!

Answer 13

yw