SOLUTION: help me solve this problem please. I don't know how to get the answers. a) How many different 7-digit numbers can be formed from the digits 0,1,2,2,3,3,3 assuming that a number

Algebra ->  Permutations -> SOLUTION: help me solve this problem please. I don't know how to get the answers. a) How many different 7-digit numbers can be formed from the digits 0,1,2,2,3,3,3 assuming that a number       Log On


   

Question 371024: help me solve this problem please. I don't know how to get the answers.
a) How many different 7-digit numbers can be formed from the digits 0,1,2,2,3,3,3 assuming that a number cannot start with 0?
ans : 360
b) how many of these numbers will end in 0?
ans : 60
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

2 is 2 times and 3 is 3 times repeated in given digits.

a) no. of ways to form 7 digit no. = 7! / ( 2! * 3!) = 420

no. of ways to form 7 digit no. having 0 at starting place = 6!/(2! * 3!) = 60
( here we have to arrange remaining 6 digits only because 0 at fixed position )

so, total no. that not start with 0 = 420-60 = 360


b)similarly to last solution

no. of ways to form 7 digit no. having 0 at last place = 6!/(2! * 3!)