We have at our disposal the following: the three letters a,b,c , and the five digits 1,2,3,4,5 . We

Jordyn Calhoun

Jordyn Calhoun

Answered question

2022-05-20

We have at our disposal the following: the three letters a,b,c , and the five digits 1,2,3,4,5 . We have to form with them all the possible passwords of six (6) characters, under the condition that there must be at least one letter and at least one number in each password. Other than this there are no more restrictions (and, thus, one can repeat at will numbers, letters and etc.)

Answer & Explanation

Lavizzariym

Lavizzariym

Beginner2022-05-21Added 10 answers

The set of elements you can choose from is this: { a , b , c , 1 , 2 , 3 , 4 , 5 }. Then you know that you will be dealing with permutations with repetition. So, the formula for permutations with repetition is n r , where n is the number of elements to choose from and r is the number of them you can choose.With all this said, then since we need to choose 6 of them from the set of 8 elements, then we have 8 6 total permutations. Now, this total includes passwords that are all numbers and all letters, so we need to subtract those from the total number of permutations.
For the total number of passwords with all letters, it is 3 6 , since there are 3 letters and we are choosing 6 of the them (all permutations with repetition allowed). This is similar for a password with all numbers, which would be 5 6 since there are 5 numbers.
This gives total possible passwords without all letters and all numbers is 8 6 5 6 3 6 = 245790

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