If you have 6 New Year greeting cards and you want to send them to 4 of your friends, in how many ways can this be done?

Correct Answer: 3439

Explanation:

The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.

 

This can be done in  10 5ways, but '0' is there

 

So, the numbers starting with '0' are to be excluded is  9 4 numbers.

 

 Total 5 digit telephone numbers =  10 5 - 9 4 = 3439

Correct Answer: 1024

Explanation:

First letter can be posted in 4 letter boxes in 4 ways. Similarly second letter can be posted in 4 letter boxes in 4 ways and so on.

Hence all the 5 letters can be posted in = 4 x 4 x 4 x 4 x 4 = 1024

Correct Answer: 2880

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 5! ways.

 

Hence, the required number of permutations  = 4! x 5! = 24 x 120 = 2880

Correct Answer: Can't determine

Explanation:

NUMERICAL has 9 positions in which 2, 4, 6, 8 are even positions.

And it contains 5 consonents i.e, N, M, R, C & L. Hence this cannot be done as 5 letters cannot be placed in 4 positions.

Therefore, Can't be determined.

Correct Answer: 3600

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

 

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

 

Correct Answer: 729

Explanation:

Choose 5 starters from a team of 12 players. Order is not important.

 

12 C 5= 729

Correct Answer: 190

Explanation:

Number of positive integral solutions =   n - 1 C r - 1 =  C 2 20 = 190

Correct Answer: 1/221

Explanation:

Total Combination of getting a card from 52 cards =  C 1 52

Because there is no replacement, so number of cards after getting first card= 51

Now, Combination of getting an another card=  C 1 51

Total combination of getting 2 cards from 52 cards without replacement= ( C 1 52 × C 1 51) 

There are total 4 Ace in stack. Combination of getting 1 Ace is =  C 1 4

 

Because there is no replacement, So number of cards after getting first Ace = 3

Combination of getting an another Ace =  C 1 3

Total Combination of getting 2 Ace without replacement= C 1 4 × C 1 3

Now,Probability of getting 2 cards which are Ace = C 1 4 × C 1 3 C 1 52 × C 1 51 = 1/221.

Correct Answer: 54

Explanation:

Number of mens = 8

Number of womens = 5

 

Different ways could couples be picked = C 1 6 × ? 9 C 1 = 9 x 6 = 54 ways.

Correct Answer: 4320

Explanation:

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.