Home » Aptitude » Permutation and Combination

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 ?

Q: 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 ?

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

7920
74841
14874
10213

Correct Answer: 7920

Explanation:

ST candidates vacancies can be filled by $C 35$ ways = 10

Remaining vacancies are 5 that are to be filled by 12

=> $C 512$ = (12x11x10x9x8)/(5x4x3x2x1) = 792

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

← Previous Question Next Question→

More Questions from Permutation and Combination

The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is
In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?
How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?
On the occasion of New Year, each student of a class sends greeting cards to the others. If there are 21 students in the class, what is the total number of greeting cards exchanged by the students?
From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?
A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?
In how many different ways can the letters of the word 'RITUAL' be arranged?
A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?
In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion