Advertisements
Advertisements
Question
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
Advertisements
Solution
A committee of 7 members is to be formed from 9 boys and 4 girls.
When there are 3 girls in that committee, then there will be 4 boys in that committee. Ways to choose 3 girls and 4 boys
= 4C3 x 9C4
= 4C1 x 9C4
[∵ 4C3 = 4C1]
= `4/1 xx (9 xx 8 xx 7 xx 6)/(1.2.3.4)`
= 9 x 8 x 7 = 504
RELATED QUESTIONS
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
12C10
f 24Cx = 24C2x + 3, find x.
If 18Cx = 18Cx + 2, find x.
If 15C3r = 15Cr + 3, find r.
If 8Cr − 7C3 = 7C2, find r.
If α = mC2, then find the value of αC2.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) no girl?
Find the number of (i) diagonals
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If nC12 = nC8 , then n =
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
The number of diagonals that can be drawn by joining the vertices of an octagon is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
If n + 1C3 = 2 · nC2 , then n =
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
If nC12 = nC8, then n is equal to ______.
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
