Advertisements
Advertisements
Question
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
Advertisements
Solution
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee 7800.
Explanation:
We have 10 men and 7 women out of which a committee of 6 is to be formed which contain atleast 3 men and 2 women
Therefore, Number of ways = 10C3 × 7C3 + 10C4 × 7C2
= `(10 xx 9 xx 8)/(3 xx 2 xx 1) xx (7 xx 6 xx 5)/(3 xx 2 xx 1) + (10 xx 9 xx 8 xx 7)/(4 xx 3 xx 2 xx ) xx (7 xx 6)/(2 xx 1)`
= 120 × 35 + 210 × 21
= 4200 + 4410
= 8610
If 2 particular women to be always present, then the number of ways = 10C4 × 5C0 + 10C3 × 5C1
= `(10 xx 9 xx 8 xx 7)/(4 xx 3 xx 2 xx 1) xx 1 + (10 xx 9 xx 8)/(3 xx 2 xx 1) xx 5`
= 210 + 120 × 5
= 210 + 600
= 810
∴ Total number of committee = 8610 – 810 = 7800
Hence, the value of the filler is 7800.
APPEARS IN
RELATED QUESTIONS
How many chords can be drawn through 21 points on a circle?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Compute:
L.C.M. (6!, 7!, 8!)
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
Evaluate the following:
If 8Cr − 7C3 = 7C2, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 16Cr = 16Cr + 2, find rC4.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
Find the number of (i) diagonals
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
Find the number of ways in which : (a) a selection
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
If 20Cr = 20Cr−10, then 18Cr is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
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.
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 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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?
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 at least one boy and one girl
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` 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 ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
