(a) P(4R,0W,0B)=(422)(47)(09)(06)
(422)=7315
(37)=3!(7−3)!7!=1(2)(3)7(6)(5)=35
(19)=9
(06)=1
P(3R,1W,0B)=731535(9)=2099
(b) P(3R,1W,0B)=(422)(37)(19)(06)
(422)=4!(22−4)!22!=1(2)(3)(4)22(21)(20)(19)=7315
(47)=4!(7−4)!7!=1(2)(3)7(6)(5)=35
(09)=1
(06)=1
P(4R,0W,0B)=731535=2091
(c) P(0R,4W,0B)=(422)(07)(49)(06)
(422)=7315
(07)=1
(49)=4!(9−4)!9!=1(2)(3)(4)9(8)(7)(6)=126
(06)=1
P(0R,4W,0B)=7315126=104518
P(0R,0W,4B)=(422)(07)(09)(46)
(422)=7315
(07)=1
(09)=1
(46)=4!(6−4)!6!=1(2)6(5)=15
P(0R,0W,4B)=731515=14633
P(all the same colour)=2091+104518+14633=
=66516 (d) P(at least one ball at each colour)=
=P(2R,1W,1B)+P(1R,2W,1B)+P(1R,1W,2B)=
(27)=21,(17)=7
(29)=36,(19)=9
(26)=15,(16)=6
P(at least one ball at each colour)=
=731521(9)(6)+73157(36)(6)+73157(9)(15)=
=5527
Comments
Dear Shiva n, you are right. Thank you for correcting us.
"Sub point d " is here any correction of calculation at last point P(2R,1W,1B) . there should be 21(9)(6) . Am i right please Re correct me if i am wrong anywhere
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