31.
In how many different ways can the letters of the word AWARE be arranged?

32.
A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associate. In how many different ways can this be done if the committee should have 2 trainees and 3 research associates?

33.
In how many different ways can the letters of the word CREAM be arranged?

34.
In how many different ways can the letters of the word ALLAHABAD be arranged?

35.
From a group of 7 men 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

36.
In how many different ways can the letters of the word BANKING be arranged in such a way that the vowels always come together?

37.
A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least 1 black ball is to be included in the draw?

38.
Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 women, and 2 men. In how many different ways can it be done?

39.
In how many different ways can the letters of the word BANANA be arranged?

40.
A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?

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