Question

Do the Question of attachment-

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Answer 1

We Have :-

A deck of cards

Solution :-

We Know :-

There are 52 cards

  26 Red :-             26 Black :-

   13 Diamond        13 Spade

   13 Heart              13 Club

( i ) Four cards of the same suit

We will add the ways of choosing them

$^{13}C_{4}+^{13}C_{4}+^{13}C_{4}+^{13}C_{4}\\\\4 * ^{13}C_{4}\\\\4 * \dfrac{13!}{4!(13-4)!}\\ \\4 * \dfrac{13!}{4!*9!} \\\\4 * \dfrac{13*12*11*10*9!}{4*3*2*1*9!} \\\\4 * \dfrac{13*12*11*10}{4*3*2*1} \\\\2860\ ways$

( ii ) Four cards belongs to four different groups

We will multiply the ways of choosing them

$^{13}C_{1}*^{13}C_{1}*^{13}C_{1}*^{13}C_{1}\\\\( ^{13}C_{1} )^{4}\\\\(\dfrac{13!}{12!})^{4}\\\\( \dfrac{13*12!}{12!})^{4}\\ ( 13 )^{4}\\\\28561\ ways$

( iii ) Are Face Cards

Number of face cards = 12 ( 3 in each suit )

$^{12}C_{4}\\\\\dfrac{12!}{4!*8!}\\ \\\dfrac{12*11*10*9*8!}{4*3*2*1*8!}$

$\dfrac{12*11*10*9}{4*3*2*1}\\ \\\ 495\ ways$

( iv ) Two are red cards and two are black cards

We will multiply there outcomes

$^{26}C_{2}*^{26}C_{2}\\\\( ^{26}C_{2})^{2}\\\\( \dfrac{26!}{2!*24!})^{2}\\ \\( \dfrac{26*25*24!}{2*1*24!})^{2}\\ \\( \dfrac{26*25}{2})^{2} \\\\( 325 )^{2}\\\\105625\ ways$

( v ) Cards of the same colour

We will add their ways

$^{26}C_{4}+^{26}C_{4}\\\\2 * ^{26}C_{4}\\\\2*\dfrac{26!}{4!*22!}\\ \\2* \dfrac{26*25*24*23*22!}{2*1*22!}\\ \\2*\dfrac{26*25*24*23}{2}\\ \\29900\ ways$

Answer 2

Answer:

We Have :-

A deck of cards

Solution :-

We Know :-

There are 52 cards

  26 Red :-             26 Black :-

   13 Diamond        13 Spade

   13 Heart              13 Club

( i ) Four cards of the same suit

We will add the ways of choosing them

( ii ) Four cards belongs to four different groups

We will multiply the ways of choosing them

( iii ) Are Face Cards

Number of face cards = 12 ( 3 in each suit )

( iv ) Two are red cards and two are black cards

We will multiply there outcomes

( v ) Cards of the same colour

We will add their ways

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