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  • How many 5-digit numbers containing the digits 1, 4, 6, 7, 9, and 8 can be created so that the digits 6 and 7 appear together?Option: 1 <p dir

How many 5-digit numbers containing the digits 1, 4, 6, 7, 9, and 8 can be created so that the digits 6 and 7 appear together?

Option: 1

300


Option: 2

301


Option: 3

310

 


Option: 4

312


Answers (1)

best_answer

There are two ways to arrange the digits 6 and 7 next to each other: we can either have 67 or 76.

For each arrangement of the digits 6 and 7, we can treat them as a single digit and then arrange the remaining digits. 

Consider the numbers 6 and 7 to be single digits. This results in a set of 5 numbers: 1, 4, 67, 9, and 8.

The number can start with any of the 5 digits, so we have 5 choices for the first digit.

For the second digit, we again have 5 choices, since we can use any of the 5 remaining digits.

For the third digit, we have only 1 choice, which is the combined digit.

For the fourth digit, we have 4 choices, since we cannot use the digit that was used for the second digit.

Finally, for the fifth digit, we have 3 choices, since we cannot use either of the digits that were used for the second or fourth digit.

Thus, the total number of 5-digit numbers that can be formed using the digits 1, 4, 6, 7, 8, and 9 such that the digits 6 and 7 appear together in the number is given by,

5\times 5\times 1\times 4\times 3\times=300

Therefore, the total number of ways the 5-digit number can be formed is 300 ways.

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