In how many ways can 4 boys and 3 girls be seated in a row if girls must sit together?

A team of 3 tennis players is to be finalized from a group of 2 male and 3 female. In how many ways this can be done and how many teams which consist of 1 male and 2 female?

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

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

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

A committee of 5 members is to be formed by selecting out of 6 men and 4 women. In how many different ways the committee can be formed if it should have at least 2 women?

Read the information given below carefully and answer the question that follows:

(A) The different ways in which the alphabets of the word BAKERY can be arranged is 720

(B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576

Choose the correct answer from the options given below: