How many permutations are there in the letters beat?

Question

1261 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-15T06:24:41

There are $24$ $24$ permutations. See explanation for details.

There are $4$ $4$ letters. The number of permutations can be calculated in $2$ $2$ ways:

The number of permutations with $n$ $n$ elements is $P_{n} = n!$ $P_n=n!$ . Here it is $P_{4} = 4! = 1 \cdot 2 \cdot 3 \cdot 4 = 24$ $P_4=4! =1*2*3*4=24$
The number of possible words can also be calculated this way:
First letter can be chosen in $4$ $4$ ways,
Second letter can only be chosen from $3$ $3$ , because one has already been used,
The third letter can be chosen from $2$ $2$ ,
The last letter is picked without any choice; there is only one letter left.

The total number of possibilities can be calculated as the product of all numbers mentioned above:

$P_{4} = 4 \cdot 3 \cdot 2 \cdot 1 = 24$ $P_4=4*3*2*1=24$