Arrange letters

[henryb]

Calculate the number of different ways in which the letters of the word, EVERMORE can be arranged.
Calculate also the number of these arrangements that begin with
(a)R
(b)E.

 

[pka]

Calculate the number of different ways in which the letters of the word, EVERMORE can be arranged.
Calculate also the number of these arrangements that begin with
(a)R
(b)E.

You have eight letters \(\displaystyle E_1E_2E_3R_1R_2VMO\). With the subscripts those are are distinct.
So with subscripts there are \(\displaystyle 8!\) ways to rearrange those eight letters.
The letters \(\displaystyle E_1E_2E_3\) can be arranged in \(\displaystyle 3!=6\) ways So if we simply remove the subscripts we have six identical strings.
There are \(\displaystyle \frac{8!}{3!\cdot 2!}\) ways to arrange the letters in \(\displaystyle EVERMORE\) because there are three identical \(\displaystyle E's\) and two identical \(\displaystyle R's\)

Now please reply telling us why \(\displaystyle \frac{11!}{(4!)^2(2!)}\) in the number of ways to rearrange the letters in \(\displaystyle MISSISSIPPI\).

 

[henryb]

You have eight letters \(\displaystyle E_1E_2E_3R_1R_2VMO\). With the subscripts those are are distinct.
So with subscripts there are \(\displaystyle 8!\) ways to rearrange those eight letters.
The letters \(\displaystyle E_1E_2E_3\) can be arranged in \(\displaystyle 3!=6\) ways So if we simply remove the subscripts we have six identical strings.
There are \(\displaystyle \frac{8!}{3!\cdot 2!}\) ways to arrange the letters in \(\displaystyle EVERMORE\) because there are three identical \(\displaystyle E's\) and two identical \(\displaystyle R's\)

Now please reply telling us why \(\displaystyle \frac{11!}{(4!)^2(2!)}\) in the number of ways to rearrange the letters in \(\displaystyle MISSISSIPPI\).

Because there are 4 identical S's and I's . Also, there are 2 identical P's

 

[henryb]

How can i solve question (a) and (b) ?

 

[pka]

How can i solve question (a) and (b) ?

Let's play the back-of-the-book game. You are in my class.
I tell you to go to the white-board with the text. In the answer section it gives:
a) \(\displaystyle \frac{7!}{3!}\) and for b) \(\displaystyle \frac{7!}{(2!)^2}\).
Now your grade for the day depends upon how well you explain to the class those answers.