English

Evaluate : n!r!(n-r)! for n = 8, r = 6

Advertisements
Advertisements

Question

Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 8, r = 6

Sum
Advertisements

Solution

n = 8, r = 6

∴ `("n"!)/("r"!("n" - "r")!) = (8!)/(6!(8 - 6)!)`

= `(8!)/(6! xx 2!)`

= `(8 xx 7 xx 6!)/(6! xx 2 xx 1)`

= 28.

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Permutations and Combination - Exercise 3.2 [Page 49]

APPEARS IN

RELATED QUESTIONS

Evaluate: 8!


Evaluate: 10!


Compute: `(12!)/(6!)`


Compute: `(12/6)!`


Compute: (3 × 2)!


Compute: 3! × 2!


Compute: `(9!)/(3!  6!)`


Compute: `(6! - 4!)/(4!)`


Compute: `(8!)/((6 - 4)!)`


Write in terms of factorial.

5 × 6 × 7 × 8 × 9 × 10


Write in terms of factorial.

6 × 7 × 8 × 9


Write in terms of factorial.

5 × 10 × 15 × 20


Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 12, r = 12


Find n, if `"n"/(8!) = 3/(6!) + (1!)/(4!)`


Find n, if `(1!)/("n"!) = (1!)/(4!) - 4/(5!)`


Find n, if (n + 1)! = 42 × (n – 1)!


Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!


Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6


Show that `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!)`


Show that `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`


Show that `((2"n")!)/("n"!)` = 2n (2n – 1)(2n – 3) ... 5.3.1


Simplify `((2"n" + 2)!)/((2"n")!)`


Simplify `(("n" + 3)!)/(("n"^2 - 4)("n" + 1)!)`


Simplify n[n! + (n – 1)!] + n2(n – 1)! + (n + 1)!


Simplify `1/(("n" - 1)!) + (1 - "n")/(("n" + 1)!)`


Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`


Select the correct answer from the given alternatives.

In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?


Select the correct answer from the given alternatives.

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate


3. 9. 15. 21 ...... upto 50 factors is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×