Sum of all 4 digit numbers formed using 6 numbers

Question

Find the sum of all four digit numbers (without repetition of digits) formed using the digits $1,2,3,4,5,6$

I have tried this problem and my answer is $\frac{5!}{2!}\times (1+2+3+4+5+6)\times (10^3+10^2+10+1)=1399860$

Am i right?

Answer 1

Well, let me check in another way

• Average digit $= 3.5$
• Average number giving place value $=3.5(1111)$
• Number of permutations $=^6P_4 = 360$
• Multiplying out, $3.5\cdot1111\cdot360 = 1399860\;\, \boxed{OK}$

PS

But while your answer is correct, the expression you have written certainly doesn't evaluate to the answer ! Did you check what your expression evaluates to ? Can you explain your expression ?

PPS

OP has later on corrected the expression to match the result.