To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

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: 120

Explanation:

In given word OLIVER there are 3 vowels E, I & O. These can be arranged in only one way as dictionary order E, I & O.

 

There are 6 letters in thegiven word.

 

First arrange 3 vowels.

 

This can be done in 6C3 ways and that too in only one way.(dictionary order E, I & O)

 

Remaining 3 letters can be placed in 3 places = 3! ways

 

Total number of possible ways of arranging letters of OLIVER = 3! x  C 3 6 ways = 6x5x4 = 120 ways.

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: 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

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: 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.