Question
Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting all the four cards of the same suit.
Answer: Option D
Four cards can be selected from 52 cards in $$^{52}{C_4}$$ ways.
Now, there are four suits, e.g. club, spade, heart and diamond each of 13 cards.
So total number of ways of getting all the four cards of the same suit:
$$\eqalign{
& { \Rightarrow ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4} \cr
& = 4{ \times ^{13}}{C_4} \cr} $$
So required probability,
$$\eqalign{
& = \frac{{4{ \times ^{13}}{C_4}}}{{^{52}{C_4}}} \cr
& = \frac{{44}}{{4165}} \cr} $$
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Four cards can be selected from 52 cards in $$^{52}{C_4}$$ ways.
Now, there are four suits, e.g. club, spade, heart and diamond each of 13 cards.
So total number of ways of getting all the four cards of the same suit:
$$\eqalign{
& { \Rightarrow ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4} \cr
& = 4{ \times ^{13}}{C_4} \cr} $$
So required probability,
$$\eqalign{
& = \frac{{4{ \times ^{13}}{C_4}}}{{^{52}{C_4}}} \cr
& = \frac{{44}}{{4165}} \cr} $$
Was this answer helpful ?
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