How many different 4 letter arrangements can be formed from the letters in the word cards

my answer: 120 arrangments

correct.

To find the number of different 4-letter arrangements that can be formed from the letters in the word "cards," we can use the formula for permutations.

The number of permutations of a set of objects is calculated by multiplying the number of available choices at each position.

In this case, we have 5 letters: c, a, r, d, s.

To form a 4-letter arrangement, we want to choose 4 letters from this set, allowing for repetition.

The number of choices for the first position is 5 (all the letters).

Similarly, for the second, third, and fourth positions, we also have 5 choices each.

So the total number of different 4-letter arrangements is calculated as follows:

Total number of arrangements = (number of choices for first position) * (number of choices for second position) * (number of choices for third position) * (number of choices for fourth position)

Total number of arrangements = 5 * 5 * 5 * 5 = 625

Therefore, there are 625 different 4-letter arrangements that can be formed from the letters in the word "cards."