In how many ways the letters of the word OLIVER be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right ?

Correct Answer: 105

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, ⁷C₁ x ⁶C₂ x ⁴C₄ 

_{= 7 x 15 x 1 = 105}

Correct Answer: 7200

Explanation:

From 5 consonants, 3 consonants can be selected in  5 C 3 ways.

 

From 4 vowels, 2 vowels can be selected in  4 C 2 ways.

 

Now with every selection, number of ways of arranging 5 letters is 5 P 5ways.

 

Total number of words =  5 C 3 * 4 C 2 * 5 P 5

 

                                = 10x 6 x 5 x 4 x 3 x 2 x 1= 7200

Correct Answer: 576

Explanation:

There are 7 letters in the word Bengali of these 3 are vowels and 4 consonants.

 

There are 4 odd places and 3 even places. 3 vowels can occupy 4 odd places in 4 P 3 ways and 4 constants can be arranged in  4 P 4 ways.

 

Number of words = 4 P 3  x  4 P 4= 24 x 24 = 576

Correct Answer: 330

Explanation:

Here the order of choosing the elements doesn?t matter and this is a problem in combinations.

 

We have to find the number of ways of choosing 4 elements of this set which has 11 elements.

 

This can be done in 11 C 4 ways = 330 ways

Correct Answer: 1440

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

Number of vowels in the given word = 2 = A & E

Required number of different ways, the letters of the word THERAPY arranged such that vowels always come together is

6! x 2! = 720 x 2 = 1440.

Correct Answer: 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed =  9 5

 

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is =  9 P 5

 

Number of words can be formed which have at least one letter repeated =   9 5 - 9 P 5

 

= 59049 - 15120

 

= 43929

Correct Answer: 7920

Explanation:

ST candidates vacancies can be filled by C 3 5 ways = 10 

Remaining vacancies are 5 that are to be filled by 12 

=> C 5 12= (12x11x10x9x8)/(5x4x3x2x1) = 792 

Total number of filling the vacancies = 10 x 792 = 7920

Correct Answer: 7! x 6!

Explanation:

The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in  7 P 6ways. 7 teachers can sit in (7-1)! ways.

 

 Required no.of ways is =  7 P 6 . 6 ! = 7 ! . 6 !

Correct Answer: 180

Explanation:

Number of ways of choosing 2 black pens from 5 black pens in 5 C 2 ways.

 

Number of ways of choosing 2 white pens from 3 white pens in  3 C 2 ways.

 

Number of ways of choosing 2 red pens from 4 red pens in 4 C 2ways.

 

By the Counting Principle, 2 black pens, 2 white pens, and 2 red pens can be chosen in 10 x 3 x 6 =180 ways.

Correct Answer: 8640