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Q:

# 5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

 A) 2880 B) 1440 C) 720 D) 2020

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

4 women can be arranged at 4 even places in 4! ways.

and 5 men can be placed in remaining 5 places in $\inline 5P_{5}$ ways.

Hence, the required number of permutations  = 4! x $\inline 5P_{5}$ = 24 x 120 = 2880

Q:

What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?

 A) 28450 B) 26340 C) 32640 D) 36450

Explanation:

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 x no of ways numbers can be formed for a number at given position x sum of all given digits

No of 1 s depends on number of digits

111 x 20 x (0+1+2+3+4+5) = 33300

We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

So the sum for this is 11 x 4 x (1+2+3+4+5).
=660

Hope u understood why we use 4. Each number can be formed in 4x1 ways

So, the final answer is 33300-660 = 32640

1 4
Q:

Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?

 A) 28 B) 56 C) 44 D) 36

Explanation:

Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by 9C2 ways i.e children.
Number of children = 9C2 = 9 x 8 / 2 = 36.

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Q:

In how many ways can the letters of the word 'LEADER' be arranged ?

 A) 360 B) 420 C) 576 D) 220

Explanation:

No. of letters in the word = 6
No. of 'E' repeated = 2
Total No. of arrangement = 6!/2! = 360

2 38
Q:

In how many different ways could couples be picked from 6 men and 9 women ?

 A) 26 B) 54 C) 52 D) 28

Explanation:

Number of mens = 8
Number of womens = 5

Different ways could couples be picked = 6c1 x 9c1 = 9 x 6 = 54 ways.

3 58
Q:

How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even ?

 A) 521 B) 720 C) 420 D) 225

Explanation:

Let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways.
so for last digit = 2, total numbers=240

Similarly for 4 and 6
When last digit = 4, total no. of ways =240
and last digit = 6, total no. of ways =240
so total of 720 even numbers are possible.