Using the digits 1, 2, 3, 5, and 6, without repetition, how many five-digit even numbers can be formed?
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Concept: Basic Principle of Counting: If there are m ways for happening of an event A, and corresponding to each possibility there are n ways for happening of event B, then the total number of different possibilities for happening of events A and B are:
Calculation: For an even number, the units place must be 2 or 6, so it can be filled in 2 ways. The remaining four places can now be filled in 4, 3, 2 and 1 ways respectively. The total number of ways in which the number can be written = 4 × 3 × 2 × 1 × 2 = 48. The digits chosen must sum to a multiple of 3, but not to a multiple of 9. If no repeated digits are allowed, the combinations of digits that have the appropriate sums are If digits are allowed to be repeated, there are 28 choices. When digits are repeated, the number of possible
variations in the digit sequence is reduced. The choices are Altogether, there are 295 different numbers that can be made with these sets of digits.
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How many 4 digit numbers can be formed from the numbers 1 3 5 7 8 and 9 which are divisible by 2 and none of the digits are repeated?How many four digit numbers can be formed from the numbers 1,3,5,7,8 and 9 which are divisible by 2 and none of the digits are repeated? 1. 60.
How many different 4 digits PINs can be produced using the digits 1 3 8 and 7?Number of PINs that can be produced using 1,3,8,7 (I assume the digits can repeat) = 4.4. 4.4=44=256.
How many 4 digit numbers can be formed using the digits 1 3 5 and 7?∴ there are 24 possible numbers that can be made using the given digits.
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