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  • The maximum number of six-digit numbers that can be created using the even number digits 2, 4, 6, and 8 when each one must appear at least once in the number is  <div c

The maximum number of six-digit numbers that can be created using the even number digits 2, 4, 6, and 8 when each one must appear at least once in the number is

 

Option: 1

1410


Option: 2

1560

 

 


Option: 3

1660

 


Option: 4

1720


Answers (1)

best_answer

Given that,

The 6-digit numbers can be formed using the even numbers 2, 4, 6, and 8.

There are two possible ways,

(i)  Each of the numbers 2, 4, 6, and 8 can be repeated three times, while the other numbers those of the types 2, 4, 6, 8, 8, and so on, can only be repeated once.

The remaining digits, such as those of the types 2, 4, 6, 6, 8, etc., repeat only once. Any two of the numbers 2, 4, 6, or 8 repeat twice.

Thus,

\frac{6 !}{3 !} \times{ }^4 C_1=480

(ii) Any two of the digits 2, 4, 6, or 8 repeat twice, while the remaining digits of the types 2, 4, 6, 6, 8, or 9 repeat only once.

\frac{6 !}{2 ! 2 !} \times{ }^4 C_2=1080

Therefore, the total number of ways is 480+1080 = 1560.

Posted by

SANGALDEEP SINGH

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