Permutation and Combination Quiz – 1

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

In a cricket championship, there are 21 matches. If each team plays one match with every other team, the number of teams is

In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is:

In how many ways can a cricket eleven be chosen out of a batch of 15 players?

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there has to be exactly 3 girls in the invitees?

24 persons shake hands with one another in a party. How many shake hands took place?

A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?

There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?