Advertisements
Advertisements
प्रश्न
Answer the following:
Find the number of words that can be formed by using all the letters in the word REMAIN If these words are written in dictionary order, what will be the 40th word?
Advertisements
उत्तर
There are 6 letters A, E, I, M, N, R
Number of words starting with A = 5!
Number of words starting with E = 5!
Number of words starting with I = 5!
Number of words starting with M = 5!
Number of words starting with N = 5!
Number of words starting with R = 5!
Total number of words = 6 × 5! = 720
Number of words starting with AE = 4! = 24
Number of words starting with AIE = 3! = 6
Number of words starting with AIM = 3! = 6
Number of words starting with AINE = 2!
Total words = 24 + 6 + 6 + 2 = 38
39th word is AINMER
40th word is AINMRE
APPEARS IN
संबंधित प्रश्न
Evaluate: 8!
Evaluate: 10!
Evaluate: 10! – 6!
Compute: (3 × 2)!
Compute: 3! × 2!
Compute: `(6! - 4!)/(4!)`
Compute: `(8!)/((6 - 4)!)`
Write in terms of factorial.
3 × 6 × 9 × 12 × 15
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 = 8, r = 6
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 (n + 3)! = 110 × (n + 1)!
Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12
Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5 : 3
Find n, if: `((2"n")!)/(7!(2"n" - 7)!) : ("n"!)/(4!("n" - 4)!)` = 24 : 1
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)!)`
Find the number of integers greater than 7,000 that can be formed using the digits 4, 6, 7, 8, and 9, without repetition: ______
If `((11 - "n")!)/((10 - "n")!) = 9,`then n = ______.
3. 9. 15. 21 ...... upto 50 factors is equal to ______.
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 – Tn = 21, then n is equal to ______.
