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 ?

Correct Answer: 125

Explanation:

Methods for selecting 4 questions out of 5 in the first section = 5 x 4 x 3 x 2 x 1/4 x 3 x 2 x 1 = 5. Similarly for other 2 sections also i.e 5 and 5

So total methods = 5 x 5 x 5 = 125.

Correct Answer: 253

Explanation:

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

Correct Answer: 325

Explanation:

Required number of signals =  5 P 1 + 5 P 2 + 5 P 3 + 5 P 4 + 5 P 5

= 5 + 20 + 60 + 120 + 120 = 325

 

 

Correct Answer: 253

Explanation:

Number of non - negative integral solutions = n + r - 1 C r - 1 = C 2 23 = 253 

Correct Answer: 1587600

Explanation:

 H   L   C   N    T    A   U   I   O

 

      L        N          A        I

 

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

 

If all the consonants  are together then the numberof arrangements =  7 ! 2 !x 1/2! .

But the 7 consonants  can be arranged themselves in   7 ! 2 ! x 1/2! ways. 

 

Hence the required number of ways =  7 ! 2 ! 2 ! 2 = 1587600

Correct Answer: 243

Explanation:

Digits are 0,1,2,3,4,5,6,7,8,9. So no. of digits are 10

 

First all possible case => 9(0 excluded) x 10 x 10 = 900

 

Second no repetition allowed =>9 x 9 x 8 = 648

 

Third all digits are same => 9 (111,222,333,444,555,666,777,888,999)

 

Three digit numbers where two of the three digits are same = 900 - 648 - 9 = 243 ;

Correct Answer: 6! x ?P?

Explanation:

We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ?P? ways.

Hence required number of ways = 6! x ?P?

Correct Answer: 531

Explanation:

Given in the question that, there are 7 boys and 6 girls. 

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

$$\begin{gathered} 6 C 3 x 7 C 2 + 6 C 4 x 7 C 1 + 6 C 5 \\ = 6 x 5 x 4 3 x 2 x 1 x 7 x 6 2 x 1 + 6 x 5 x 4 x 3 4 x 3 x 2 x 1 x 7 + 6 x 5 x 4 x 3 x 2 5 x 4 x 3 x 2 x 1 \\ = 420 + 105 + 6 \\ = 531 . \end{gathered}$$

Correct Answer: 164

Explanation:

For a triangle, we need 3 non-collinear points. So with 12 points (when all the 12 are such that any three non-collinear is 12 C 3. But among them 8 points are collinear.

 

If all these 8 points are different we get  8 C 3 triangles as they are collinear.

 

In  12 C 3 triangles, we do not get  8 C 3 triangles

 

Therefore, The number of triangles we get = 12 C 3 - 8 C 3 = 164

Correct Answer: 17280

Explanation:

There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.

 

Similarly, there are 5 novels.They can be arranged in 5! ways.

 

And there are 3 plays.They can be arranged in 3! ways.

 

So, by the counting principle all of them together can be arranged in 4!´5!´3! ways = 17280