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: at least 3 girls?
Advertisements
Solution
If there are at least 3 girls in the committee then the committees will be formed as follows:
- 3 girls, 4 boys
- 4 girls, 3 boys
Total ways of forming these committees = 4C3 x 9C4 + 4C4 x 9C3
= 4C1 x 9C4 + 1 x 9C3
= `4 xx (9 xx 8 xx 7 xx 6)/(1 xx 2 xx 3 xx 4) + (9 xx 8 xx 7)/(1 xx 2 xx 3)`
= 504 + 84
= 588
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
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.
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
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?
If nC4 = nC6, find 12Cn.
If 8Cr − 7C3 = 7C2, find r.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If α = mC2, then find the value of αC2.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
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?
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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 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?
Find the number of (ii) triangles
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?
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.
Find the number of ways in which : (a) a selection
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?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 20Cr = 20Cr−10, then 18Cr is equal to
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together 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 student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Find the value of 15C4
Find the value of 15C4 + 15C5
Find the value of 20C16 – 19C16
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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 six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
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 no girls
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 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 ______.
