Advertisements
Advertisements
Question
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Solution
`""^"n""P"_"r"` = 720
∴ `("n"!)/(("n" - "r")!)` = 720 ...(i)
Also, `""^"n""C"_("n" - "r")` = 120
∴ `("n"!)/(("n" - "r")!("n"-"n"+"r")!) = 120`
∴ `("n"!)/("r"!("n" - "r")!)` = 120 ...(ii)
Dividing (i) by (ii), we get
∴ `(("n"!)/(("n"-"r")!))/(("n"!)/("r"!("n"-"r")!))=720/120`
∴ r! = 6
∴ r = 3
Substituting r = 3 in (i), we get
∴ `("n"!)/(("n" - 3)!)` = 720
∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!)` = 720
∴ n(n – 1)(n – 2) = 10 × 9 × 8
∴ n = 10
APPEARS IN
RELATED QUESTIONS
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Compute:
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 odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
Evaluate the following:
14C3
Evaluate the following:
n + 1Cn
Evaluate the following:
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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: atmost 3 girls?
Find the value of 15C4 + 15C5
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
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 at least three girls.
In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
