Four cards are drawn from a well shuffled deck of 52 cards. Number of ways to draw four cards of same denomination `=alpha` and number of ways to draw four cards of different denomination `=beta`. Which of following is correct?

Options

A. `(beta)/(alpha)` is divisible by 13.
B. `beta+alpha` is divisible by 13
C. `beta-alpha` is divisible by 13
D. `beta` is divisible by `(13)^(2)`

Answer

B, C

Explanation

(i). `alpha="4kings"+"4 quenns" +"4 Jake"+"4lo's' +___+"4Ace"`
`=^(4)C_(4)+^(4)C_(4)+___+ .^(4)C_(4)=13`
(ii). `beta=` select any for denomination out of 13 and draw one card for each.
`beta=^(13)C_(4).^(4)C_(1).^(4)C_(1).^(4)C_(1).^(4)C_(1)`
Correct option is (B), (C)