How many distinguishable permutations can be made from the letters in the word 'RECALL'?

To determine the number of distinguishable permutations of the letters in the word 'RECALL', we start by identifying how many letters are in the word and whether any of these letters are repeated.

The word 'RECALL' consists of 6 letters: R, E, C, A, L, L. Here, we notice that the letter 'L' appears twice, while all other letters (R, E, C, A) are unique.

When calculating the distinguishable permutations, we would typically use the formula:

[

\text{Number of permutations} = \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!}

]

where ( n ) is the total number of letters, and ( p_1, p_2, \ldots, p_k ) are the counts of each repeating letter.

In this case:

• ( n = 6 ) (the total number of letters in 'RECALL')

• The letter 'L' repeats 2 times, so we will divide by ( 2! ).

Putting this into the formula gives us:

[

\text{Number of distinguishable permutations} = \frac