Advertisements
Advertisements
Question
How many different selections of 5 books can be made from 12 different books if, Two particular books are never selected?
Solution
Two particular books are never selected.
Since two books are never selected.
The total number of books is 10.
∴ The number of ways of selecting 5 books from 10 books
= 10C5
= `(10!)/(5! xx (10 - 5)!)`
= `(10!)/(5! xx 5!)`
= `(10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5! xx 5!)`
= `(10 xx 9 xx 8 xx 7 xx 6)/(5!)`
= `(10 xx 9 xx 8 xx 7 xx 6)/(5 xx 4 xx 3 xx 2 xx 1)`
= 2 × 9 × 2 × 7
= 252 ways
APPEARS IN
RELATED QUESTIONS
How many triangles can be formed by joining the vertices of a hexagon?
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.
If nC3 = nC2 then the value of nC4 is:
The number of ways selecting 4 players out of 5 is
There are 10 true or false questions in an examination. Then these questions can be answered in
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"!)`
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 4 elements
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] n elements
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly three aces in each combination
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of at least 3 women?
How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?
Choose the correct alternative:
The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together 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
