The number of binary relations on a set with $$n$$ elements is:

The number of binary strings of $$n$$ zeros and $$k$$ ones such that no two ones are adjacent is:

(a) Mr. X claims the following:
If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof.

"From xRy, using symmetry we get yRx. Now because R is transitive, xRy and yRx togethrer imply xRx. Therefore, R is reflextive."

Briefly point out the flaw in Mr. X' proof.

(b) Give an example of a relation R which is symmetric and transitive but not reflexive.

Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers among themselves?