Question

Find the number of different ways of
arranging letters in the word ARRANGE.
How many of these arrangements the two
R's and two A's are not together?​

Answer 1

Answer:

7! - 5!/(2!*2!)

Step-by-step explanation:

we will take the case of two R and two A together and minus it from total case ,then will get no R no A together

...

total no of ways =7!

Now take take 2R and 2A together hence 5! is no of ways in which 2R 2A N G E can be arranged and as 2R and 2A are alike so divide by 2! and 2!

Answer 2

consider AA and RR as one letter .

then we 5letters such as

AA RR N G E

and

AA and RR should not come together

therefore first arrange N G and E

_N_G_E_

there are 4 vacant spaces

there fore it can be arranged in

4p2 ways=12 ways

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