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A child has plastic toys bearing the digits 4, 4 and 5. How many 3-digit numbers can he make using them?

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Given: 

We have toys with bearing 4, 4 and 5 

To Find: Number of 3-digit numbers he can make 

The formula used: The number of permutations of n objects, where p1 objects are of one kind, p2 are of the second kind, ..., pk is of a kth kind and the rest, if any, are of a 

different kind is = \(\frac{n!}{P_1!p_2! ......P_k!}\)

The child has to form a 3-digit number. 

Here the child has two 4’s. 

We have to use the above formula 

Where, 

n = 3

p1 = 2

\(\frac{3!}{2!}\) = 3 ways

The numbers are 544, 454 and 445. 

He can make 3 3-digit numbers.

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