In how many ways can we distribute 5 distinct balls, $${B_1},{B_2},......,{B_5}$$ in 5 distinct cells, $${C_1},{C_2},.....,{C_5}$$ such that Ball $${B_i}$$ is not in cell $${C_i}$$, $$\forall i = 1,2,....,5$$ and each cell contains exactly one ball?

The recurrence equation
$$\,\,\,\,\,\,\,T\left( 1 \right) = 1$$
$$\,\,\,\,\,\,T\left( n \right) = 2T\left( {n - 1} \right) + n,\,n \ge 2$$
evaluates to

How many 4 digit even numbers have all 4 digits distinct?

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