By using 2, 4, 5, 7, 8, 9 how many three digit numbers are formed in form xyz when x + y + z is even. (repitition not allowed).Correct answer is '60'. Can you explain this answer?

Question

Answer

(3 - even) or (2 – odd and 1 - even)
³C₃ × 3! + ³C₂ × ³C₁ × 3! = 60
(Total numbers).

Answer

(3 - even) or (2 – odd and 1 - even)
³C₃ × 3! + ³C₂ × ³C₁ × 3! = 60
(Total numbers).

Answer

Given:
We are given the digits 2, 4, 5, 7, 8, and 9.

To Find:
We need to determine the number of three-digit numbers that can be formed in the form xyz, where x, y, and z are even digits.

Solution:
To solve this problem, we can break it down into three cases:

Case 1: When x is even
In this case, x can only be either 2, 4, or 8. Once x is chosen, there are 3 remaining digits (including 0) available for y. Similarly, there are 2 remaining digits available for z. Therefore, the total number of three-digit numbers that can be formed in this case is:
3 choices for x x 3 choices for y x 2 choices for z = 18

Case 2: When y is even
In this case, y can only be either 2, 4, 8. Once y is chosen, there are 2 remaining digits available for x (excluding the chosen y) and 2 remaining digits available for z. Therefore, the total number of three-digit numbers that can be formed in this case is:
3 choices for y x 2 choices for x x 2 choices for z = 12

Case 3: When z is even
In this case, z can only be either 2, 4, 8. Once z is chosen, there are 2 remaining digits available for x and 2 remaining digits available for y. Therefore, the total number of three-digit numbers that can be formed in this case is:
3 choices for z x 2 choices for x x 2 choices for y = 12

Total:
To find the total number of three-digit numbers, we sum up the results from all three cases:
18 (case 1) + 12 (case 2) + 12 (case 3) = 42

However, we need to note that the problem specifies that repetition is not allowed. Since we have used all 6 given digits in the calculations above, there are no repetitions. Therefore, every possibility is unique.

Hence, the correct answer is 42.

Similar JEE Doubts

By using 2, 4, 5, 7, 8, 9. How many three digit numbers are formed in form xyz when x < y and z < y (Repition not allowe d) :- Correct answer is '40'. Can you explain this answer?

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The sum of all the four digit even numbers which can be formed by using the digits 0,1,2,3,4 and 5 if repetition of digits is allowed is:?

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