If two cards are taken one after another without replacing from a pack of 52 car

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Question
If two cards are taken one after another without replacing from a pack of 52 cards. What is the probability for the two cards be Ace ?
Options
A. 51/1221
B. 42/221
C. 1/221
D. 52/1245

Correct Answer

1/221

Explanation

Total Combination of getting a card from 52 cards = ${}^{52}C_{1}$

Because there is no replacement, so number of cards after getting first card= 51

Now, Combination of getting an another card= ${}^{51}C_{1}$

Total combination of getting 2 cards from 52 cards without replacement= ( ${}^{52}C_{1} � {}^{51}C_{1}$ )

There are total 4 Ace in stack. Combination of getting 1 Ace is = ${}^{4}C_{1}$

Because there is no replacement, So number of cards after getting first Ace = 3

Combination of getting an another Ace = ${}^{3}C_{1}$

Total Combination of getting 2 Ace without replacement= ${}^{4}C_{1} � {}^{3}C_{1}$

Now,Probability of getting 2 cards which are Ace = $\frac{{}^{4}C_{1} � {}^{3}C_{1}}{{}^{52}C_{1} � {}^{51}C_{1}}$ = 1/221.

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CAT