In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?

Correct Answer: 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. 

 

(i) 1 lady out of 4 and 4 gentlemen out of 6 

(ii) 2 ladies out of 4 and 3 gentlemen out of 6 

(iii) 3 ladies out of 4 and 2 gentlemen out of 6 

(iv) 4 ladies out of 4 and 1 gentlemen out of 6 

 

In case I the number of ways =  C 1 4 × C 4 6 = 4 x 15 = 60 

In case II the number of ways =  C 2 4 × C 3 6 = 6 x 20 = 120 

In case III the number of ways =  C 3 4 × C 2 6 = 4 x 15 = 60

In case IV the number of ways =  C 4 4 × C 1 6 = 1 x 6 = 6 

 

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

Correct Answer: 720

Explanation:

The number of letters in the given word RITUAL = 6

Then, 

Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!

=> 6 x 5 x 4 x 3 x 2 x 1 = 720

Correct Answer: 15/26

Explanation:

Number of cards in a pack of cards = 52

Number of black cards = 26

Number of king cards = 4 (2 Red, 2 Black)

 

Required, the probability that if a card is drawn either card is black or a king = 

26 52 + 4 52 = 30 52 = 15 26

Correct Answer: 27404

Explanation:

Given total 16 Red roses and 14 White roses = 30 roses

 

Four flowers have to be selected from 30 i.e,   C 4 30= 27405 Ways 

 

Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses)  = 27404 ways. 

Correct Answer: 420

Explanation:

Given total number of students in the class = 21

 

So each student will have 20 greeting cards to be send or receive (21 - 1(himself))

 

Therefore, the total number of greeting cards exchanged by the students = 20 x 21 = 420.

Correct Answer: 36

Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

 

Let us mark these positions as under: 

                                                      (1) (2) (3) (4) (5) (6) 

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.  

Number of ways of arranging the vowels = 3 P 3 = 3! = 6.

 

Also, the 3 consonants can be arranged at the remaining 3 positions. 

Number of ways of these arrangements =  3 P 3 = 3! = 6. 

Total number of ways = (6 x 6) = 36.

Correct Answer: 17576

Explanation:

The first letter from the right can be chosen in 26 ways because there are 26 alphabets.

 

Having chosen this, the second letter can be chosen in 26 ways

 

The first two letters can chosen in 26 x 26 = 676 ways

 

Having chosen the first two letters, the third letter can be chosen in 26 ways.

 

All the three letters can be chosen in 676 x 26 =17576 ways.

 

It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.

Correct Answer: 5^10

Explanation:

Each of the 10 letters can be posted in any of the 5 boxes.

 

So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.

 

i.e. 5*5*5*?.*5 (upto 10 times) = 5 ^ 10.

Correct Answer: 60

Explanation:

Given letters are k, l, m, n, o = 5

number of letters to be in the words = 3

Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters =  5 P 3 ways .

? 5 P 3 = 5 x 4 x 3 = 60 words .

Correct Answer: 15 × 13 × 13!

Explanation:

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= 15 × 13 × 13!