1.

In how many different number of ways 4 boys and 2 girls can sit on a bench?

**Answer: Option ''**

**Answer: Option 'C'
^{n}p_{n} = n!
^{6}p_{6}
= 6 × 5 × 4 × 3 × 2 × 1 = 720**

2.

In how many different number of ways 5 men and 2 women can sit on a shopa which can accommodate persons?

**Answer: Option 'D'**

**Answer: Option 'D' **

^{7}p_{3} = 7 × 6 × 5 = 210

3.

In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.

**Answer: Option 'A'**

**Answer: Option 'A'**

4.

In how many different ways can the letters of the word "CLAIM" be rearrangement?

**Answer: Option 'A'**

**Answer: Option 'A'
The total number of arrangements is
**

5.

If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE.

**Answer: Option 'C'**

**Answer: Option 'C'
Total no'of arrangements ^{5}P_{5} = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.**

6.

How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?

**Answer: Option ''**

**Answer: Option 'B'
E,I fixed. Consonants can be arrangements in ^{3}P_{3} = 3! = 6 ways**

7.

If all the numbers 2, 3, 4, 5, 6, 7, 8 are arranged, find the number of arrangements in which 2, 3, 4, are together?

**Answer: Option 'A'**

**Answer: Option 'A'
If (2 3 4) is one.
we must arrange (2 3 4), 5, 6, 7, 8 in
**

8.

Find ^{10}P_{6}

**Answer: Option ''**

**Answer: Option 'B'
^{10}P_{6} = 10!/4! = 10 × 9 × 8 × 7 × 6 × 5
= 151200.**

9.

Find ^{9}P_{3}

**Answer: Option 'B'**

^{9}P_{3} = 9!/6! = 9 × 8 × 7

= 504.

10.

Find ^{7}P_{7}

**Answer: Option 'B'**

^{7}P_{7} = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

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