## 26. In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?

## 27. How many numbers are there between 100 and 1000 such that at least one of their digits is 6?

## 28. A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?

## 29. While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible?

## 30. How many positive integers 'n' can be form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 60,00,000?

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