There are 120 ways to arrange the digits {1, 3, 5, 6, 7} to create a

Question

There are 120 ways to arrange the digits {1, 3, 5, 6, 7} to create a five-digit number such that each number is picked at random and can only be used once. If those five-digit numbers are listed in order from smallest to largest, what is the 26th term in the set?

A. 17,651
B. 31,567
C. 31,576
D. 31,657
E. 31,675

A. 17,651
B. 31,567
C. 31,576
D. 31,657
E. 31,675

Gladiator59 · Accepted Answer

There are 5! = 120 ways to arrange the digits to form 5-digit numbers.

While arranging from smallest to largest, the smallest numbers will begin with 1. 1(followed by 4! = 24) will be the first 24 5-digit numbers.

The 25th number will be the smallest number starting with 3. which will be 3 followed by rest digits in ascending order. { 31,567 is 25th term in set}

Hence the  26th term will be 31,576 .

Hence  Option (C)  is our answer.

Best,
Gladi

push12345 · Answer

Take 13 _ _ _ 3!
 15 _ _ _ 3!
 16 _ _ _ 3! 
 17 _ _ _ 3!
This constitute 24 terms next term would start with 31
 31567
Next would be 31576 this is 26 the term

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Fdambro294 · Answer

There are 120 ways to arrange the 5 Distinct Digits to make 5 Digit Numbers.

Symmetry Concept: Each Digit has an equal probability of landing in each of the Digit Spots. So 1/5th of the 120 Numbers will have the Digit 1 in the TEN THOUSANDS Place

1/5 * 120 = 24 Numbers will have 1 in the TEN THOUSANDS Place and these will be the 1ss 24 Smallest Value Integers when all the Possible Numbers are listed in Ascending Order.

The next Largest Value Numbers will have the Digit 3 in the Ten Thousands Place.

Therefore, the 25th Number will be the LOWEST Value Number we can make with 3 in the Ten Thousands Place =

31, 567

the 26th Number will therefore be the NEXT Lowest Value Number we can make with 3 in the Ten Thousands Place =

31, 576

Answer -C-

MathRevolution · Answer

The first number will start from 1 _ _ _ _: for 4 spaces we have 4! ways to arrange the numbers = 24 ways or 24 numbers are done.

25^{th}  number will start from 3 and in order to be a five-digit number to be minimum second digit will be 1 and third will be 5, the fourth will be 6 and the fifth digit will be 7: 315 67

Hence,the  26^{th}  number will have interchange between '6' and '7': 315 76 .

Answer C

bumpbot · Answer

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There are 120 ways to arrange the digits {1, 3, 5, 6, 7} to create a

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