The sum of five digit numbers which can be formed with the digits $$3$$, $$4$$, $$5$$, $$6$$, $$7$$ using each digit only once in each arrangement, is

Question

Infinity Learn · Accepted Answer

The number of numbers of five digits, having $$3$$ in unit’s place $$=4P4$$ (number$$ of arrangements of the remaining four $$digits)=$$ $$4$$! $$=$$ $$24$$.Similar is the case for other digits, i.e., each digit occurs $$24$$ times in the unit’s place.Hence, the sum of the digits in unit’s $$place=24$$×$$3+24$$×$$4+24$$×$$5+24$$×$$6+24$$×$$7=24(3+4+5+6+7)=24$$×$$25=600Similarly$$, the sum of the digits in each of the other places $$=$$ $$600$$.∴ The required $$sum=600$$×$$10000+600$$×$$1000+600$$×$$100+600$$×$$10+600$$×$$1$$ $$=600(10000+1000+100+10+1) $$=600$$×$$11111=6666600$$.

The sum of five digit numbers which can be formed with the digits 3, 4, 5, 6, 7 using each digit only once in each arrangement, is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material