In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

A bank has 6 digit account number with no repetition of digits within a account number. The first and last digit of the account numbers is fixed to be 4 and 7. How many such account numbers are possible?

A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. The probability that both the marbles are of the same color is,

How many 3-letter words can be formed out of the letters of the word 'CORPORATION', if repetition of letters is not allowed?

In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?

In the principle of mathematical induction, which of the following steps is mandatory?

What is the induction hypothesis assumption for the inequality m !> 2m where m>=4?

For every natural number k, which of the following is true?

In how many ways can 8 different dolls be packed in 5 identical gift boxes such that no box is empty if any of the boxes hold all of the toys?

In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?

When four coins are tossed simultaneously, in _______ number of the outcomes at most two of the coins will turn up as heads.

A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?

If the objects are arranged in a circle or closed curve is called as

Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.

Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.

How many words can be obtained from the word 'PHOTOGRAPH'

How many different bit strings are there of length six?

What is the number of arrangements of all the six letters in the word PEPPER?

How many permutations are there in the word MISSISSIPPI?