Q. 205.0( 1 Vote )
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 this committee would consist of 1 man and 2 women?
Answer :
Given that we need to select 3 persons out of 2 men and 3 women,
Let us assume the no. of ways of selecting be N,
⇒ N = selecting 3 persons out of total 5 persons
⇒ N = 5C3
We know that
And also n! = (n)(n – 1)(n – 2)…………2.1
⇒
⇒
⇒
⇒ N = 10 ways
The no. of ways of selecting 3 persons out of 2 men and 3 women is 10.
(ii) It is told that 1 man and 2 women should be selected out of 2 men and 3 women.
Let us assume the no. of ways of selection be N1,
⇒ N1 = (selecting one man out of 2 men) × (selecting 2 women out of 3 women)
⇒ N1 = (2C1) × (3C2)
We know that
And also n! = (n)(n – 1)(n – 2)…………2.1
⇒
⇒
⇒
⇒ N1 = 6 ways
The no. of ways of selecting 1 man and 2 women is 6.
Rate this question :






















How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
RD Sharma - MathematicsA 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?
RD Sharma - MathematicsHow many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
4 letters are used at a time
RD Sharma - MathematicsA parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
RD Sharma - MathematicsHow many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if
all letters are used at a time
RD Sharma - MathematicsOut of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines (ii) triangles can be formed by joining them?
RD Sharma - Mathematics