Question

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Answer 1

6. The word ‘COMMITTEE’ has 9 letters.

So it can be permuted in 9 ways, but we’ve got letters repeating there. To avoid the same arrangements happening again, we eliminate the repetitions.

M repeats twice. T Twice. E twice.

7. If it must be greater than 2000 , the first digit must either be 2 or 3 , which means you will have 2 choices. After that, there will be 3 choices for the second digit. Then there will be 2 choices for the third digit. Lastly there will be just 1 choice for the last digit.

The number of permutations becomes 2×3×2×1=12 .

Explanation:

Answer 2

#6

The word has 9 letters with 2 Ms, 2Ts and 2Es

We need 2 Ts together, this reduces the number of positions by one.

The number of ways:

• (9-1)!/2!2! = 8!/4 = 10080

#7

Digits 0, 1, 2, 3

Number should be greater than 2000, it means the number is:

• 2xxx ⇒ 3P3 = 3! = 6 ways

or

• 3xxx ⇒ 3P3 = 3! = 6 ways

Total permutations:

• 2*6 = 12