there are 8 people in a committee. each time they meet they shake hands with each other so that each person shakes everyones hand once
each time they meet how many handshakes are there
8 * 7 = ?
divide that by 2, since it takes two hands to shake once.
Well, let's do some handshaky math here. If there are 8 people in the committee, then each person needs to shake hands with the other 7 people. So, the first person shakes hands with 7 others, the second person shakes hands with 6 remaining people, and so on.
If we add up all the handshakes:
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 handshakes
So, each time they meet, there are 28 handshakes going on! That's a lot of shaking, but it's a great way to build team spirit, don't you think?
To find the number of handshakes each time they meet, we can use a combination formula.
Since there are 8 people in the committee, each person needs to shake hands with 7 other people (as they cannot shake hands with themselves).
The combination formula to find the number of handshakes is given by:
nCr = n! / (r! * (n-r)!)
Where n is the total number of people and r is the number of people involved in each handshake.
In this case, n = 8 and r = 2 (since each handshake involves 2 people).
Plugging in the values into the formula:
8C2 = 8! / (2! * (8-2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!) / (2! * 6!)
= (8 * 7) / 2
= 56 / 2
= 28
Therefore, each time they meet, there are 28 handshakes.
To find the number of handshakes each time they meet, we need to consider the number of unique pairs that can be formed from a group of 8 people.
The formula to find the number of unique pairs is (n * (n - 1)) / 2, where n is the number of people. In this case, n = 8.
Plugging in the values, the number of handshakes each time they meet is:
(8 * (8 - 1)) / 2 = 8 * 7 / 2 = 56 / 2 = 28
Therefore, there are 28 handshakes each time the committee meets.