One night, 4 friends talked on the telephone. Each friend talked to each of their other friends once. How many conversations took place?

Answer 1

for a group of

2 friends, just one conversation

for

3 friends 3 conversations

for

4 friends 6 conversations

4C2 = 4!/2!2!= 4x3/2x2 = 6

combinations of 4 taken 2 at a time =6 or more generally

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

It's also the 5th row of Pascal's triangle or the coefficients of a binomial to the 4th power, (x+y)^4

1,3,6,6,3,1

1

11

121

1331

14641 x^4 + 4x^3y + 6 x^2y^2 + 4xy^3 + y^4 = (x+y)^4