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

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

e.

step-by-step explanation:

because there are always 10 numbers in a phone number.

p = 6s

step-by-step explanation: