(19)

5 times the sum of missing number should be less than 36.

If 1 digit is missing = 7

If 2 digit is missing = 9

If 3 digit is missing-2

If 0 digit is missing = 1

Alternate

A is subset of S hence

A can have elements:

type 1 : { }

type 2: {E 1 }, {E 2 },......{E 8 }

type 3: {E l , E 2 },{E 1 ,E 3 }......{E 1 ,E 8 }

.

.

.

type 6: {E 1 , E 2 ,.......E 5 },.......{E 4 , E 5 , E 6 , E 7 , E 8 }

type 7: [E 1 , E 2 ,.......E 6 ],.......{E 3 , E 4 ,...........E 8 }

type 8: {E 1 , E 2 ,.......E 7 }{E 2 ,E 3 ,.........E 8 }

type 9: {E 1 , E 2 ,.......E 8 }

As ;

Note : Type 1 to Type 4 elements can not be in set A as maximum probability of type 4 elements.

{E 5 ,E 6 , E 7 ,E 8 }is

Now for Type 5 acceptable elements let's call probability as P 5

n 1 +n 2 +n 3 +n 4 +n 5 28.8

Hence, 2 possible ways {E 5 , E 6 , E 7 , E 8 , E 3 or E 4 }

P 6 = n 1 + n 2 + n 3 + n 4 + n 5 + n 6 28.8

9 possible ways

1 possible ways

P 8 n 1 + n 2 +..........+ n 8 28.8

1 possible way

Total = 19

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