Fill in the blanks

1. …………… devised the method of induction.
2. …………… is used to prove that the sum of first n positive integers equals n^{2}sup>?
3. The properties of integer can be proved by ………………?
4. The case or exception which fails the mathematical formula or statement is
called ……………?
5. The ………….. of a formula is established if it is true for each element of set
under consideration?
6. The method of mathematical induction is used to avoid ……………?

The Governor of Punjab calls a meeting of 12 officers. In how many ways can they be seated round a table? The members of a club are 12 boys and 8 girls. In how many ways can a committee of 3 boys and 2 girls be formed? Two fair dice, one red and the other blue, are rolled simultaneously. The numbers on the tops are added.

Find the probability when the total of two scores is i. 5 ii.11? A card is drawn from a deck of 52 playing cards. What is the probability that it is a diamond card or an ace? A fair die is thrown twice. Find the probability that a prime number of dots appear in the first throw and the number of dots in the second throw is less than 5?