In how many ways we can select 5 cards from a deck of 52 cards, if each selection must include atleast one king

Let us select 5 cards first. This can be done in ⁵²C₅ ways.

total no. of cards having no kings = ⁴⁸C₅ ways.

thus, total ways (having atleast 1 king) = (⁵²C₅ - ⁴⁸C₅)ways