CBSE Class 11-science Answered

Dear Student

We have t 0 use 0,1,2,3 at least once in the six digit number.

So first we have to choose 4 places among 6 to put these 4 digits (0, 1, 2, 3).This can be done in  6P₄ways.  6P₄= 6!/(6-4)! = 6X5X4X3X2X1     /    2X1   = 360     (“! “Denotes factorial)

There are 2 more places left in the six digit number, since there is no restriction on re use of 0, 1, 2, 3 we can choose the remaining 2 digits from ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)  there are 10P₂ ways to do this.

10P₂=10! / (10-2)! = 90

Total number of all six digit numbers = 360X90=324000

We should not consider the number s starting with “0” as six digit number.

If “0” at the first position there are 5 more digits remained in the six digit number. Those 5 digits can be arranged in 5! Ways, i.e. 150.

324000-150=323850

So total number of six digit numbers is 323850.

Regards

Team

Topper learning