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?

Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of $$k$$ colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $$k$$ that satisfies this requirement?

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?