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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 arrange
Question
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? Answering this question requires using both the multiplication rule and the addition rule . The answer to the question is
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Mathematics
5 years
2021-09-01T07:00:07+00:00
2021-09-01T07:00:07+00:00 1 Answers
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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