Question

There are six children playing card game. How many ways are there to deal hands of five cards to each of the 6 players from 52 cards.

Answer 1

Solution:

We are giving 5 cards to each players from 52 cards

first we need to find selection of 5 cards from 52 cards

selection of first hand of 5 cards = ⁵²P₅

Selection of second first hand of 5 cards = ⁴⁷P₅

Selection of third hand of 5 cards = ⁴²P₅

Selection of 4th hand of 5 cards = ³⁷P₅

selection of 5th hand of 5 cards = ³²P₅

Selection of 6th hand of 5 cards = ²⁷P₅

So

there are total deal hands of five cards to each of the 6 players from 52 cards.

= ⁵²P₅ x ⁴⁷P₅ x ⁴²P₅ x ³⁷P₅ x ³²P₅ x ²⁷P₅