First slide

Combinations

Question

The number of five digit numbers that can be formed by using digits 1, 2, 3 only, such that three digits of the formed number are identical, is

Moderate

A

30
B

60
C

120
D

90

Solution

When exactly three digits are identical and the remaining two are different, then the number of such numbers
$(^{3} C_{1}) (\frac{5!}{3!}) = 60$
When three digits are identical and the remaining two are also identical, then the number of ways
$= (^{3} C_{2}) (2) (\frac{5!}{3! 2!}) = 60$
Thus, the number of such numbers $= 120 .$

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