Advertisement Remove all ads

Find n if: n!3!(n-3)!:n!5!(n-5)! = 5:3 - Mathematics and Statistics

Sum

Find n if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5:3

Advertisement Remove all ads

Solution

`("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5:3

∴ `("n"!)/(3!("n" - 3)!)xx(5!("n"-5)!)/("n"!) = 5/3`

`∴("n"!)/(3!("n"-3)("n"-4)("n"-5)!) xx(5xx4xx3!("n"-5)!)/"n!"=5/3`

∴ `(5xx4)/(("n" - 3)("n" - 4)) = 5/3`

∴ (n – 3) (n – 4) = `(20 xx 3)/(5)`

∴ (n – 3) (n – 4) = 12
∴ (n – 3) (n – 4) = 4 × 3
Comparing on both sides, we get
∴ n – 3 = 4
∴ n = 7

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 8. (i) | Page 76
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×