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."