How many different 4 letter arrangements can be formed from the letters in the word cards
To find the number of different 4-letter arrangements that can be formed from the letters in the word "cards," we can use the concept of permutations.
In this case, we have 5 letters: c, a, r, d, and s. We want to find the number of arrangements of 4 letters.
To calculate this, we can use the formula for permutations, which is given by:
P(n, r) = n! / (n - r)!
where P(n, r) represents the number of arrangements of r items from a set of n items, and the exclamation mark (!) denotes factorial.
Using this formula, we can substitute n = 5 (the number of letters) and r = 4 (the number of letters we want to arrange), giving us:
P(5, 4) = 5! / (5 - 4)! = 5! / 1! = 5 x 4 x 3 x 2 = 120
Therefore, there are 120 different 4-letter arrangements that can be formed from the letters in the word "cards."
To find the number of different 4-letter arrangements that can be formed from the letters in the word "cards," we can use the concept of permutations.
In this case, we have 5 letters (c, a, r, d, s) to choose from and we need to select 4 of them at a time.
The formula to calculate the number of permutations is:
P(n, r) = n! / (n - r)!
where P(n, r) represents the number of permutations of n items taken r at a time, and the exclamation mark (!) denotes factorial.
Using the formula, we can calculate the number of different 4-letter arrangements:
P(5, 4) = 5! / (5 - 4)!
= 5! / 1!
= (5 * 4 * 3 * 2 * 1) / 1
= 120 / 1
= 120
Therefore, there are 120 different 4-letter arrangements that can be formed from the letters in the word "cards."