Counting methods

[manelgirona]

How many people are in room A?

1. A total of 15 different pairs of people can be selected from the people in the room
2. If there were one fewer person in room A, a total of different pairs of people could be selected from room A

I don't know how to solve it

Answer D

[ajith]

How many people are in room A?

1. A total of 15 different pairs of people can be selected from the people in the room
2. If there were one fewer person in room A, a total of different pairs of people could be selected from room A

I don't know how to solve it

Answer D

Say there are n number people in the room.

1. The num of ways in which one can select different pairs from n number of people is nC2
nC2 =15 => n(n-1)/2 =15 => n =6; Sufficient
2. There is a number missing in the highlighted part
nevertheless this number will be the number of ways in which we can select two from a set of n-1 = n-1C2 = (n-1)(n-2)/2
we can find n from that number which is missing also, Sufficient

D

[manelgirona]

Sorry. I forgot the number. You were right

2. If there were one fewer person in room A, a total of 10 different pairs of people could be selected from room A

[ajith]

Sorry. I forgot the number. You were right

2. If there were one fewer person in room A, a total of 10 different pairs of people could be selected from room A

(n-1)C2 = 10

(n-1)(n-2)/2 =10

(n-1)(n-2) = 20 = 5*4

n-1 =5
n=6