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?
Advertisements
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.
How many chords can be drawn through 21 points on a circle?
There are 18 guests at a dinner party. They have to sit 9 guests on either side of a long table, three particular persons decide to sit on one side and two others on the other side. In how many ways can the guests to be seated?
In how many ways can a cricket team of 11 players be chosen out of a batch of 15 players?
- There is no restriction on the selection.
- A particular player is always chosen.
- A particular player is never chosen.
From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?
Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is:
Prove that `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4` = 40C5
Prove that `""^(2"n")"C"_"n" = (2^"n" xx 1 xx 3 xx ... (2"n" - 1))/("n"!)`
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?
A trust has 25 members. How many ways 3 officers can be selected?
How many different selections of 5 books can be made from 12 different books if, Two particular books are always 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 student is excluded?
In an examination a student has to answer 5 questions, out of 9 questions in which 2 are compulsory. In how many ways a student can answer the questions?
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 joining 15 points on the plane, in which no line joining any three points?
A polygon has 90 diagonals. Find the number of its sides?
Choose the correct alternative:
The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is
Choose the correct alternative:
The number of rectangles that a chessboard has ______
Choose the correct alternative:
If nC4, nC5, nC6 are in AP the value of n can be
