Advertisements
Advertisements
Question
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?
Advertisements
Solution
A committee of 3 people is to be constituted from a group of 2 men and 3 women.
∴ Number of ways =\[{}^2 C_0 \times^3 C_3 +^2 C_1 \times^3 C_2 + {}^2 C_2 \times^3 C_1 = 1 + 2 \times 3 + 3 \times 1 = 10\]
Number of committees consisting of 1 man and 2 women =\[{}^2 C_1 \times^3 C_2 = 6\]
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
How many chords can be drawn through 21 points on a circle?
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?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Compute:
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?
How many three-digit numbers are there with no digit repeated?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
Evaluate the following:
If 28C2r : 24C2r − 4 = 225 : 11, find r.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
How many triangles can be obtained by joining 12 points, five of which are collinear?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =
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
The value of\[\left( \ ^{7}{}{C}_0 + \ ^{7}{}{C}_1 \right) + \left( \ ^{7}{}{C}_1 + \ ^{7}{}{C}_2 \right) + . . . + \left( \ ^{7}{}{C}_6 + \ ^{7}{}{C}_7 \right)\] is
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.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 20C16 – 19C16
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
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?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 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 ______.
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 ______.
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 ______.
