a password consists of 3 letters from a to f inclusive and 4 digits from 0 to 9 inclusive.each letter and digit can only be usd once.how many different password can be formed?
Question
a password consists of 3 letters from a to f inclusive and 4 digits from 0 to 9 inclusive.each letter and digit can only be usd once.how many different password can be formed?
Solution
To solve this problem, we need to use the concept of permutations.
Step 1: Calculate the number of ways to choose the letters.
There are 6 letters from a to f inclusive. We need to choose 3 out of these 6. Since the order matters and each letter can only be used once, we use the formula for permutations which is nPr = n! / (n-r)!. Here, n is the total number of options (6 letters) and r is the number of options to choose (3 letters). So, 6P3 = 6! / (6-3)! = 120.
Step 2: Calculate the number of ways to choose the digits.
There are 10 digits from 0 to 9 inclusive. We need to choose 4 out of these 10. Again, since the order matters and each digit can only be used once, we use the formula for permutations. So, 10P4 = 10! / (10-4)! = 5040.
Step 3: Combine the two.
Since the letters and digits can be arranged in any order, we multiply the number of ways to choose the letters by the number of ways to choose the digits. So, the total number of different passwords that can be formed is 120 * 5040 = 604800.
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