10 directors all shook hands with each other. How many

Question

10 directors all shook hands with each other.
How many handshakes were performed?

Explain your answer.

jimjohn · Answer

or another way to look at it is:

the first person has 9 people who he shakes hands with
the second has 8 people plus the handshake with the first person which we already counted
the third had 7 people plus the two handshakes that we alreaedy counted
....
so its 9+7+6+5+4+3+2+1 = 45

gmatraider · Answer

Can anyone expalin why it is 10c2? what about the wording suggests the 2? thanks.

walker · Answer

paraphrase our question:

How many unique pairs can we choose from 10 people regardless order in a pair?

C^{10}_2

tejal777 · Answer

A handshake is performed between "TWO" ppl..to hands are needed to perform a handshake..so out of 10 ppl we have to choose 2 who will shake hands..So,10c2

lawschoolsearcher · Answer

These things used to confuse me until I learned about Anagram.
It's like rearranging the alphabet HHNNNNNNNN

H represents handshake
N represents no handshake

So how many ways we can get two people handshaking in a group of 10 people?

10!/2!8!= 10x9/2 = 9x5 =45

subhashghosh · Answer

10C2 = 10!/8!2! = 90/2 = 45

ravsg · Answer

Number of people required for a handshake = 2
so, number of people available for one side = 10
Number of people available to complete the pair = 9

Here pair AB is the same as BA
so, 10 x 9 /2
45

10 directors all shook hands with each other. How many

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