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Question

The number of integers between 1 and $${ 10 }^{ 6 }$$ have the sum of their digits equal of K : $$\left( where\quad 1<k<18 \right) $$

A

$$^{ \left( K+6 \right) }{ C }_{ 6^{ - } }^{ (K-4) }{ C }_{ 6 }$$

B

$$^{ K }{ C }_{ 6 }-6.^{ K }{ C }_{ 4 }$$

C

$$^{ K }{ C }_{ 6 }-6.^{ K-4 }{ C }_{ 6 }$$

D

None of these

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Solution

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Correct option is A. $$^{ \left( K+6 \right) }{ C }_{ 6^{ - } }^{ (K-4) }{ C }_{ 6 }$$

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