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how many numbers less than 4321, can be formed from the digits 1,2,3,4,if repetition is allowed?
The answer is 340.
232
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 wayssimilarly, 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
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