Question

a ) If I draw 14 cards from a standard deck of 52, will there be a pair?

b ) Given a text file with 500,000 words of size 4 or less, is it possible that the words are distinct?

PLEASE EXPLAIN BOTH PARTS THOROUGHLY, THANKS IN ADVANCE

Answer 1

a. Note that by a pair means one king and one queen in same sign.

If you draw 14 cards form a deck of 52 cards you might not end up with a pair. For example you can get 12 cards of diamond (except queen) and number 1 and 2 from club. This draw does not guarantee to have a pair.

b. To give the answer of this question we will calculate the total number of distinct words can be made with 4 or less letters. If the number is less than 500,000 then clearly we can't have all distinct words if the number is greater than 500,000 then we might have distinct words.

Number of distinct words can be made with 4 or less letters = number of distinct words can be made with 4 letters + number of distinct words can be made with 3 letters + number of distinct words can be made with 2 letters + number of distinct words can be made with 1 letter.

number of distinct words can be made with 1letter = 26

number of distinct words can be made with 2 letters = .

number of distinct words can be made with 3 letters =

number of distinct words can be made with 4 letters =

Hence the number of distinct words can be made with 4 letters or less is .

Thus its not possible all words are distinct.

Feel free to comment if you have any doubts. Cheers!