Advertisements
Advertisements
Question
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
Options
45
350
4200
230
Advertisements
Solution
350
Explanation:
Out of 7 men, 3 men can be chosen in 7C3 ways and out of 5 women
2 women can be chosen in 5C2 ways.
Hence, the committee can be chosen in 7C3 × 5C2 = 350 ways.
APPEARS IN
RELATED QUESTIONS
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
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?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Evaluate the following:
n + 1Cn
Evaluate the following:
If nC10 = nC12, find 23Cn.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
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 products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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?
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 (ii) at least one boy and one girl?
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?
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
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?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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: atmost 3 girls?
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?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
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 can be of any colour
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 ______.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship 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 ______.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
