Permutations and Combinations

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Question

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Question 1 :

There are 12 points in a plane out of which 5 are collinear. The number of triangles formed by the points as vertices is

1. 185
2. 210
3. 220
4. 175
Answer
7975

Question 2 :

The number of combination of n distinct objects taken r at a time be x is given by

1. ^n/2C_r
2. ^n/2C_r/2
3. ⁿC_r/2
4. ⁿC_r
Answer
7976

Question 3 :

Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is

1. 1296
2. 671
3. 625
4. 585
Answer
7977

Question 4 :

If repetition of the digits is allowed, then the number of even natural numbers having three digits is

1. 550
2. 450
3. 350
4. 250
Answer
7978

Question 5 :

The number of ways in which 8 distinct toys can be distributed among 5 children is

1. 5⁸
2. 8⁵
3. ⁸P₅
4. ⁵P₅
Answer
7979