Permutation and combinations (Trig/alg2 class)
In how many ways can all the letters in SEYCHELLES be arranged?
To determine the number of ways the letters in SEYCHELLES can be arranged, we can use the concept of permutations.
Permutations involve arranging objects in a specific order. In this case, we want to arrange the letters in the word SEYCHELLES.
The word SEYCHELLES has 10 letters. To calculate the number of permutations, we can use the formula for permutations of n objects taken r at a time:
P(n, r) = n! / (n - r)!
Where n represents the total number of objects (in this case, the number of letters in the word SEYCHELLES), and r represents the number of objects taken at a time (which is equal to n in this case, since we want to arrange all the letters). The exclamation mark (!) denotes factorial, which is the product of all positive integers less than or equal to a given number.
Plugging in the values, we have:
P(10, 10) = 10! / (10 - 10)!
= 10! / 0!
Any number divided by 0 is undefined, so 0! is defined as 1.
Therefore, the number of ways the letters in SEYCHELLES can be arranged is:
P(10, 10) = 10! / 0!
= 10! / 1
= 10!
Calculating 10!:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 3,628,800
Therefore, there are 3,628,800 ways to arrange the letters in SEYCHELLES.