Find the number of distinguishable permutations of the letters in the word ambassador?

Question

Anyone know how to solve this?

Answer 1

There are 10 letters so you need 10! (that's the factorial sign meaning 10*9*8*...*3*2*1)

The "a" repeats 3 times so you need to divide by 3!

The "s" repeats 2 times so you need to divide by 2!

10! / (3! * 2!) = 10! / (6 *2) = 10! / 12 = 302400 ways

Answer 2

The total number of permutations for the word "ambassador" (containing 10 letters) is 10!
This number is however diminished by two factors: 3! for the 3 a's and 2! for the 2 s's.
The required answer is therefore 10!/(3!*2!)

Answer 3

Distinguishable Permutations

Answer 4

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RE:
Find the number of distinguishable permutations of the letters in the word ambassador?
Anyone know how to solve this?

Answer 5

The formula you need is the multinomial formula. If there are k letters, and k1 are repeated, and then k2 are repeated, etc, the total number of permutations is

(k!)/([(k1)!(k2)!...(kt)!},

where t is the number of disticct letters.

In the case of "ambassador", there are

k1 - 3 a's

k2 = 2 s's,

and b, d, m, o, r are distinct letters.,

for a total of 10 letters.

So, the answer is

10!/[2! 3! 1! 1! 1! 1! 1!] = 3628800/[2X6X1X1X1]

=302,400 distinguishable permutations.

Answer 6

First, pretend EVERY letter is different, and compute how many ways you can form a 10-letter word from them. The first letter of the word can be one of 10, the second one of the remaining 9, etc.
So there are 10! (factorial) combinations if every letter were different.

However, since there are three "a"s and 2 "s"s, you have fewer unique combinations. How may ways can you sort the three "a"s? (6), and the two s's (2)
so I think the answer is 10!/(2*6)

Answer 7

10! / (3!*2!) = 302,400

That's the answer!! :)