Question

Number of natural numbers upto one lakh which contains 1, 2, 3 exactly once and remaining digits any time is

Answer 1

Number of natural numbers upto one lakh which contains 1, 2, 3 exactly once and remaining digits any time is 2940

Step-by-step explanation:

Step 1:

Given data:

100000

we can say that 3 digit 3! = 6

since we know that 4 digit without zero $= 6c1\times 4! = 144$

and with zero $= 3c1\times3! = 18$

Step 2:

5 digit = without zero$= 5c3* 3! \times 36 = 2160$

with 1 zero =$4c1.4! \times 6= 576$

with 2 zero $= 4c2\times 3!=36$

Thus the Number of natural numbers upto one lakh which contains 1, 2, 3 exactly once and remaining digits any time is calculated by the following

total = 6 + 144 + 18 + 2160 + 576 + 36 = 2940

Therefore the answer is 2940

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