# how many numbers less than 4321, can be formed from the digits 1,2,3,4,if repetition is allowed?

34 Points
11 years ago

The answer is 340.

Kolla Raja Sekhar
51 Points
11 years ago

232

Md Rizwan
33 Points
11 years ago

when the thousands place is fixed as 1 ,  then the number formed is 1...       with repitition allowed, the three places can be filled in 4*4*4= 64 ways
similarly, fixing 2 at the thousands place, we have 4*4*4 =64 ways of forming a four digit - number
also fixing 3 at the thousands place we have 64 four-digit numbers
fixing 4 at the thousands place, we can have the hundreds place in 3 ways , but the tens place can be filled only in 1 way because we cannot have 2 or 3 or 4 at the tens position as per the condition given .   and the units place can be filled in 4 ways
so, total number of ways of forming  a four digit number under the condition given to us =64 +64+64+ 3*4 = 204 ways
but we can form 1 digit number in 4 ways, two digit numbers in 4*4=16 ways, three digit numbers in 4*4*4 = 64 ways, so total numbers we can form = 204+4+16+64