SOLUTION: A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and

Question 1026955: A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and the other two, once each. How many different numbers are possible.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Choose the digit that appears four times (7 ways), then choose the remaining two digits (say A and B). Assume that A and B are chosen with order important (6*5 = 30 ways) - you will see why later.

Choose four of the six placeholders for the digit that appears four times to occupy (6C4 = 15 ways). Then put A (the first of the 2 digits chosen) in the first unoccupied spot and B in the second unoccupied spot. This constructs such a number, and we know that we didn't overcount.

# of ways = 7*30*15 = 3150

RELATED QUESTIONS
Suppose repetitions are not allowed. Answer the following: a) Find how many three-digit... (answered by ewatrrr)

How many 7-digit numbers can be formed using the digits 1, 2, 3, 4, and 5, provided that... (answered by Edwin McCravy,ikleyn,mccravyedwin)

How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never... (answered by Edwin McCravy)

A security code is to be formed by using three alphabets and four digits chosen from the (answered by Edwin McCravy)

A security code is to be formed by using three alphabets and four digits chosen from the... (answered by ikleyn)

A 3-digit number will be formed using the numbers 2, 3, 4, 5, and 7. How many are less... (answered by macston)

Hello, Given a sey of digits 1 to 9. 9 digit numbers are to be formed from the set... (answered by greenestamps)

I saw this solution online from a tutor (ikelyn). I think there's a mistake in it and i... (answered by math_tutor2020,ikleyn)

How many different digit numbers can be formed using the integers 1,2,3,4? There are 8 (answered by mark_henrhiz)