Question

How many different ways are there to arrange the letters A, B, A, and B? 4 6 8 16

Answer 1

There are 6 different possible arrangements of letters A, B, A, B.

Solution:

Need to determine different ways to range letters A, B, A and B.

Using the theorem which says that the number of permutation of n alphabets, where $p_1$ number of alphabets of one kind and $p_2$ is number of alphabets of second kind is given by following formula.

Number of possible arrangements $=\frac{n !}{p_{1} ! \times p_{2} !} \rightarrow(1)$

In our case total number of alphabets = n = 4

Number of letter A = $p_1$ = 2

Number of letter B = $p_2$ = 2

Using (1), we get

Number of possible arrangements of A, B, A, B $=\frac{4 !}{2 ! \times 2 !}=\frac{4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1}=3 \times 2=6$

Hence there are 6 different possible arrangements of letters A, B, A, B.