A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ballis 14400, then n is equal to
6
5
4
3
The number of five digit numbers divisible by 5 that can be formed using the numbers 0, 1, 2, 3, 4, 5 without repetition is
240
216
120
96
B.
216
The five digit number is formed only when unit place is either 0 or 5.
Case I. When 0 is in unit place, then rest of numbers can be selected in ways.
= 5! = 120
Case II. When 5 is in unit place, then rest of numbers can be selected in ways
= 5! = 120
And we have to subtract those cases in which 0 is in thousand place.
The number of ways = = 24
Required number of ways = 120 + 120 - 24 = 216
10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated, is
11! 10!
If tn denotes the number of triangles formed with n points in a plane, no three of which are collinear and if tn + 1 - tn= 36, then n is equal to
7
8
9
10
Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, is
296
540
408
348