Using inductive reasoning, write a formula for the number of handshakes if the number of people is n.?

Question

PLEASE HELP ME WITH HOMEWORK!

Answer 1

take n to equal 10 people, ok
first person can shake 9
second can shake 8 (since one used up before)
third can shake 7 (since shook 1st and 2nd)
so total number will be 9+8+7+6+5+4+3+2+1=45
or in terms of 10, handshakes equals n/2 times n-1
for 9 people it would be 9/2 times 8 = 36
got it? (n/2)*(n-1)

Answer 2

answer is n(n-1)/2 if n>=2

if n=2, there is only one handshake and the formula is correct(check by substituting)

Assume the result is true for n=k persons in the room

that is k(k-1)/2 handshakes if there are k persons in the room.

Now assume that a new person comes in the room and shakes hands with the k persons already present in the room

so that now with k+1 persons in the room there are

[ { k(k-1)/2} +k ]handshakes

that is { k(k+1)/2} handshakes (on simplification)

that is { (k+1)[(k+1)-1] / 2} handshakes if there are k+1 persons in the room.


therefore the result is true for n=k+1 provided it is true for n=k.
the result has been proved for n=2. etc. etc.

Answer 3

2 people A and B : 1 handshake
3 people A, B, C: 3 = 2+1 handshakes
(AB=BA, AC=CA, and BC=CB)
4 people A, B, C, D: 6 = 3+2+1 handshakes
(AB, AC, AD, BC, BD, CD)
5 people A, B, C, D, E: 10 = 4+3+2+1handshakes
(AB, AC, AD, AE, BC, BD, BE, CD, CE, DE)
Continuing in this fashion, it follows that the number of handshakes between n people is :
(n-1) + (n-2) +...+2+1 = n*(n-1)/2

Answer 4

sum of the natural numbers from 1 to n is n*(n-1)/2 here the sum is from 1 to n-1 so the formula is

(n-1)*(n-2)/2

Answer 5

n to the 2nd power. each person can shake with either hand. as each new person arrives the first person can shake either of the new persons hands with either of their own hands and so on.

Answer 6

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

or in this case

nC2 = (n!)/(2!(n - 2)!)

or just

nC2 = (n!)/(2(n - 2)!)

so it all depends on the number of people.