Question

11. How many permutations of all the letters of the word "TRIGONOMETRY“.
A.29,937,600 b.194,800 c..59,875,200 d.498,960​

Answer 1

Given :- How many permutations of all the letters of the word "TRIGONOMETRY“.

A) 29,937,600

B) 194,800

C) 59,875,200

D) 498,960

Answer :-

we have,

• Total letters in TRIGONOMETRY = 12 .
• O = 2 times .
• T = 2 times .
• R = 2 times .

so,

→ Total permutations = 12! / (2! * 2! * 2!)

→ Total permutations = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2!) / (2! * 2! * 2!)

→ Total permutations = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3) / (2 * 2)

→ Total permutations = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 3

→ Total permutations = 59,875,200 (C) (Ans.)