1. How many three different digit numbers could be formed from the set ofDigits {1, 3, 6, 7}?(a) 9 (b) 12 (c) 64 (d) 24
Question
How many three different digit numbers could be formed from the set of Digits {1, 3, 6, 7}?
(a) 9
(b) 12
(c) 64
(d) 24
Solution
The solution to this problem involves the concept of permutations.
Step 1: Understand the problem We are asked to find out how many three-digit numbers can be formed from the set of digits {1, 3, 6, 7}. The numbers must be different and the digits in the numbers must also be different.
Step 2: Apply the concept of permutations In permutations, the order of the digits matters. For a three-digit number, we have three places to fill: the hundreds place, the tens place, and the ones place.
Step 3: Calculate the permutations For the hundreds place, we have 4 choices (1, 3, 6, or 7). After filling the hundreds place, we have 3 choices left for the tens place. And after filling the tens place, we have 2 choices left for the ones place.
So, the total number of different three-digit numbers that can be formed is 432 = 24.
Therefore, the answer is (d) 24.
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