Advertisements
Advertisements
प्रश्न
How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?
उत्तर
Number of persons = 10
Number of committee members to be selected = 6
A committee must have a chairperson and a secretary, the remaining 4 members.
The number of ways of selecting a chairperson and a secretary from 10 persons is
= 10C2
= `(10!)/(2!(10 - 2)!)`
= `(10!)/(2! 8!)`
= `(10 xx 9 xx 8!)/(2! xx 8!)`
= `(10 xx 9)/(2 xx 1)`
= 5 × 9
= 45
After the selection of chairperson and secretary remaining number of persons = 8
Number of ways of selecting remaining 4 committee members from the remaining 8 persons
= 8C4
= `(8!)/(4!(8 - 4)!)`
= `(8!)/(4! xx 4!)`
= `(8 xx 7 xx 6 xx 5 xx 4!)/(4! xx 4!)`
= `(8 xx 7 xx 6 xx 5)/(4!)`
= `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1)`
= 2 × 7 × 5
= 70
∴ A number of ways of selecting the six committee members from 10 persons.
= 45 × 70
= 3150 ways
APPEARS IN
संबंधित प्रश्न
If nPr = 1680 and nCr = 70, find n and r.
Verify that 8C4 + 8C3 = 9C4.
A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when
- atleast two ladies are included.
- atmost two ladies are included.
In how many different ways, 2 Mathematics, 2 Economics and 2 History books can be selected from 9 Mathematics, 8 Economics and 7 History books?
If nC3 = nC2 then the value of nC4 is:
The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:
There are 10 true or false questions in an examination. Then these questions can be answered in
Prove that `""^(2"n")"C"_"n" = (2^"n" xx 1 xx 3 xx ... (2"n" - 1))/("n"!)`
Prove that if 1 ≤ r ≤ n then `"n" xx ""^(("n" - 1))"C"_("r" - 1) = ""^(("n" - "r" + 1))"C"_("r" - 1)`
A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?
How many different selections of 5 books can be made from 12 different books if, Two particular books are never selected?
There are 5 teachers and 20 students. Out of them a committee of 2 teachers 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 teacher is included?
There are 5 teachers and 20 students. Out of them a committee of 2 teachers 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 excluded?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination
Find the number of ways of forming a committee of 5 members out of 7 Indians and 5 Americans, so that always Indians will be the majority in the committee
Find the number of strings of 4 letters that can be formed with the letters of the word EXAMINATION?
How many triangles can be formed by 15 points, in which 7 of them lie on one line and the remaining 8 on another parallel line?
There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, the number of straight lines that can be obtained from the pairs of these points?
Choose the correct alternative:
In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is
