Advertisements
Advertisements
Question
How many committee of five persons with a chairperson can be selected from 12 persons.
Advertisements
Solution
Total number of Persons = 12
Number of persons to be selected = 5
Out of 5, there is a chairperson
∴ Number of ways of selecting a chairperson = 12C1 = 12
Number of ways of selecting other 4 numbers out of remaining 11 persons = 11C4
∴ Total number of ways = 12C1 × 11C4
= `12 xx (11*10*9*8)/(4*3*2*1)`
= 12 × 330
= 3960
Hence, the required number of ways = 3960.
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Prove that
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?
How many three-digit odd numbers are there?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
If nC12 = nC5, find the value of n.
f 24Cx = 24C2x + 3, find x.
If 8Cr − 7C3 = 7C2, find r.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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?
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(iii) at least 3 girls?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Find the number of (i) diagonals
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?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
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
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Find the value of 15C4 + 15C5
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.
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 three girls.
15C8 + 15C9 – 15C6 – 15C7 = ______.
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 ______.
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 ______.
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 ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
