As Jamie purchased a laptop for his compulsory schoolwork, he tried creating a password with a high level of security, so he chose 5 alpha-numeric symbols that contain the numbers 1-5 and the vowels 'a', 'e', 'i', 'o', and 'u'. If this case contains at least one number and one letter, what are the different permutations?
To find the different permutations, we can use the concept of counting principles. In this case, Jamie has chosen 5 symbols from a set of alphanumeric symbols, which includes numbers 1-5 and the vowels 'a', 'e', 'i', 'o', and 'u'.
To calculate the number of permutations, we need to consider the different possible positions for each symbol. Since we have 5 symbols and 5 positions, the total number of permutations can be calculated using the formula for permutation:
nPr = n! / (n-r)!
Where n is the total number of symbols (5) and r is the number of symbols chosen (5).
Let's calculate the number of permutations:
5P5 = 5! / (5-5)!
= 5! / 0!
= 5! / 1
= 5 x 4 x 3 x 2 x 1 / 1
= 120
Therefore, there are 120 different permutations possible for Jamie's password.