Permutation and Combination Test 4

In how many different ways can the letters of the word ‘APPLE’ be arranged?

In how many different ways can the letters of the word CORPORATE be arranged so that the vowels are adjacent to each other?

A box contains 8 white balls, 3 red balls and 5 black balls. In how many ways can 7 balls be selected so that there is at least 2 balls of each colour?

In how many ways 3 prizes can be given to 7 boys?

In how many different ways can the letters of the word ‘SECOND be arranged?

In how many different ways can the letters of the word ‘HAPPY’ be arranged having both P’s together?

Find the probability of getting at most 1 head when 3 coins are tossed simultaneously?

Three dies were tossed simultaneously. What is the probability of getting the same number on all the three dices?

In how many ways can a group of 4 boys and 4 girls be chosen from a batch consisting of 6 boys and 5 girls?

 Which of these numbers can’t be a probability?

 There is a pack of 52 cards and Ajay draws two cards together, what is the probability that one is spade and one is heart?

Two cards are drawn, without replacement, from an ordinary pack of cards. Find the probability that at least one of the cards is red.

What is the probability of solving a given problem if three students (A, B and C), try it independently, with respective probabilities 

 An urn contains 7 red and 5 green marbles. If four marbles are picked at random, what is the probability that two are green and two are red?

 An urn contains 7 green and 5 yellow balls. Two balls are drawn at a time. The probability that both balls are of same colour is