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Let $f : A \to B$ be a function where set A contains 4 elements and set B contains 3 elements. Number of functions defined from $A \to B$ which are not surjective is also equal to:

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number of natural number solutions of the equation $x + y + z = 11.$

number of ways in which 10 children can be divided into two groups one containing 2 and other containing 8 children.

number of ways in which 4 boys and 4 girls can be arranged alternately in a circle

total number of divisors of the number 3600.

answer is A, B, D.

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Detailed Solution

Total functions $= 3^{4} = 81$
Now, into functions = Total functions-onto functions
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$= 81 - \frac{4!}{1! 1! 2!} . \frac{1}{2!} \times 3! = 81 - 36 = 45$

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