2. In how many ways can letters in the word PALINDROME be arranged using:
a. 3 letters at a time? c. 5 letters at a time?
b. 6 letters at a time? d. all letters?
Answers
Given : word PALINDROME
To Find : how many ways letters can be arranged
a. 3 letters at a time
b. 6 letters at a time
c. 5 letters at a time
d. all letters
Solution:
PALINDROME
= 10 letters
Assuming no repetition of letters
a. 3 letters at a time
3 letters out of 10 can be arranged in ¹⁰P₃ = 10 * 9 * 8 = 720 ways
b. 5 letters at a time
5 letters out of 10 can be arranged in ¹⁰P₅ = 10 * 9 * 8 * 7 * 6 =30240 ways
c. 6 letters at a time
6 letters out of 10 can be arranged in ¹⁰P₆ = 10 * 9 * 8 * 7 * 6 * 5 =151200 ways
d. all letters
= 10 !
= 36,28,800 ways
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