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Q:

# What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?

 A) 2856 B) 3969 C) 480 D) None of these

Explanation:

We can select atleast one item from 6 different items = $\inline&space;(2^{6}-1)$

Similarly we can select atleast one item from other set of 6 different items in $\inline&space;(2^{6}-1)$ ways.

$\therefore$ Required number of ways = $\inline&space;(2^{6}-1)(2^{6}-1)$

= $\inline&space;(2^{6}-1)^2$ = 3969

Q:

There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical ?

 A) 23 B) 432 C) 22 D) 431

Explanation:

As in this problem , buying any fruit is different case , as buying apple is independent from buying banana.
so ADDITION rule will be used.
9C1 + 8c1 + 6c1 = 23 will be answer.

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Q:

There are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made ?

 A) 49450 B) 50540 C) 46587 D) 52487

Explanation:

Given G + B= 41 and B = G-1
Hence, G = 21 and B = 20
Now we have 2 options,
1G and 3M
(or)
3G and 1M
(2G and 2M or 0G and 4M or 4G and oM are not allowed),

Total : 21C1 x 20C3 + 21C3x20C1 = 50540 ways.

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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

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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