SOLUTION: a) find the number of ways the word HISTORY can be arranged. b) Find the number of ways the word HISTORY can be arranged if the letters O and R are (i) together, (il) not togeth

Question 1203281: a) find the number of ways the word HISTORY can be arranged.
b) Find the number of ways the word HISTORY can be arranged if the letters
O and R are (i) together, (il) not together
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
a) find the number of ways the word HISTORY can be arranged.

7! = 5040
ways

b) Find the number of ways the word HISTORY can be arranged if the
letters O and R are
(i) together,

There are 

1.  6 things: H, I, S, T, OR, Y to arrange in 6! = 720 ways

Plus

2.  6 things: H, I, S, T, RO, Y to arrange in 6! = 720 ways

for a total of 1440 ways.

(il) not together

(Number of arrangements of HISTORY) - (number of arrangements O and R are together.)  

That's

5040 - 1440 = 3600 ways.

Edwin

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