Four different digits are chosen from the set {1,2,3,5,6,7} and then arranged to form a four...

Four different digits are chosen from the set {1,2,3,5,6,7} and then arranged to form a four digit number. How many even numbers that are greater than 4000 can be formed?

Solutions

Expert Solution

The first digit can be filled with 3 ways i.e. 5, 6 or 7

The last digit can be filled with 2 ways i.e. 2 or 6.

Even Numbers starting with 5 = 2 * 4 * 3 = 24

Even Numbers starting with 6 = 4 * 3 = 12

Even Numbers starting with 7 = 2 * 4 * 3 = 24

Even numbers that are greater than 4000 can be formed = Even Numbers starting with 5 + Even Numbers starting with 6 + Even Numbers starting with 7

= 24 + 12 + 24

= 60 (ans)

orchestra answered 1 year ago

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