(a) To log on to a certain computer account, the user must type in a 3-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 3 -letter passwords are possible? (There are 26 letters in the alphabet.)□(b) From a collection of 52 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?□
Q. (a) To log on to a certain computer account, the user must type in a 3-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 3 -letter passwords are possible? (There are 26 letters in the alphabet.)□(b) From a collection of 52 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?□
Calculate Password Possibilities: Calculate the number of possible 3-letter passwords where no letter repeats and only lowercase letters are used. There are 26 choices for the first letter, 25 for the second (since it can't repeat the first), and 24 for the third (can't repeat the first two). Calculation: 26×25×24.
Verify Password Calculation: Check the calculation for any errors. 26 choices for the first letter, 25 for the second, and 24 for the third are correctly considered without repetition.
Calculate Customer Selection: Calculate the number of ways to choose 2 customers from a group of 52. This is a combination problem, not permutation, since the order of selection doesn't matter. Calculation: 52 choose 2, which is rac{52!}{2! * (52-2)!}.
Simplify Customer Selection Calculation: Simplify the calculation for choosing 2 customers. 2!×50!52! simplifies to 2×152×51=1326.
Check Customer Selection Calculation: Check the calculation for any errors. The formula for combinations (k=k!⋅(n−k)!n!n) is correctly applied, and the arithmetic is correct.
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