## Permutations Combinations Probablity IB math HL

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### Permutations Combinations Probablity IB math HL

Permutations Combinations Probability- IB Mathematics HL – IB maths HL

How can we find the number of different arrangements of the letters of the word “LONDON”? and how can we calculate the probability of the event that the middle two letters both are N’s?

Thanks
Jack

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Joined: Mon Jan 28, 2013 8:08 pm

### Re: Permutations Combinations Probablity IB math HL

Permutations, Combinations, Probability - IB Maths HL

The number of different arrangements of the six letters from which there are two pairs of same letters is given by the following formula

$\frac{6!}{2!2!}= \frac{720}{4}=180$

Since the two N’s are located in the middle of the word there are $\frac{4!}{2!}= \frac{24}{2}=12$ ways to arrange the remaining 4 letters from which there are two O,s .
So, the probability equals to $\frac{12}{180}=\frac{1}{15}$

Hope these help!!
elizabeth

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Joined: Mon Jan 28, 2013 8:09 pm

### Re: Permutations Combinations Probablity IB math HL

Thank you Elisabeth!
Jack

Posts: 0
Joined: Mon Jan 28, 2013 8:08 pm