Answer:
a) Total number of ways can the letters of the word MINUTES be arranged in a row = 5040
b) Total number of ways in which M and I must remain next to each other = 1440
Step-by-step explanation:
To find - Refer to the solution to Exercise 9.3.11 to answer the following
questions.
(a) How many ways can the letters of the word MINUTES
be arranged in a row?
(b) How many ways can the letters of the word MINUTES
be arranged in a row if M and I must remain next to each
other as either MI or IM?
Proof -
a)
Given that , the word is - MINUTES
We can see that all the words are different.
So, Total number of ways they can arrange in a row = 7!
= 7×6×5×4×3×2×1
= 5040
⇒Total number of ways can the letters of the word MINUTES be arranged in a row = 5040
b)
Given word is - MINUTES
Given that , M and I must remain next to each other
So, treat them as 1 word
If IM appears then
Total number of words = 6
So, they can arrange in 6! ways
Also,
MI appears then
Total number of words = 6
So, they can arrange in 6! ways
∴ we get
Total number of ways in which M and I must remain next to each other = 6! + 6! = 720 + 720 = 1440
⇒Total number of ways in which M and I must remain next to each other = 1440
