A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4  and 5 without repetitions. The total number of ways this can be done is
(A) 216
(B) 600
(C) 240
(D) 3125

Every body in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is
(A) 11
(B) 12
(C) 13
(D) 14

The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is
(A) 105
(B) 15
(C) 175
(D) 185

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
 (A) 6
(B) 18
(C) 12
(D) 9

The number of 5-digit telephone numbers having atleast one of their digits repeated is
(A) 90,000
(B) 10,000
(C) 30,240
(D) 69,760

The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is
(A) 94
(B) 126
(C) 128
(D) None

The total number of 9 digit numbers which have all different digits is
(A) 10!
(B) 9 !
(C) 9 × 9!
(D) 10×10!

Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is
(A) 3600
(B) 3720
(C) 3800
(D) 3600

The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.

The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.

Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls.The number of ways in which this can be done if at least 2 are red is ______