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1. In how many ways can the letters of the word ‘CAR’ be reordered to produce distinct ‘words’?

2. How many different strings can be made from the letters in ‘ENGINEERING’ using all the letters?

3. Find the coefficient of 11 in the expansion of (3 − 22)12?

4. A pair of fair dice is tossed. Find the probability that one of the dice is 3, if the sum is 5?

5. Are the event , that a family with three children has children of both sexes, and that a family with three children has at most one boy, independent? Assume that the eight ways a family can have three children are equally likely.

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