Question

Number of ways in which 12 different things can be divided among five persons so that they get 2,2,2,3,3 things respectively

Answer 1

Please see the attachment

Answer 2

$Total \:number \: of \: things = 12$

$12 \: things \: are \: to \: be \: divided \: into \\5 \: persons \: get \: 2,2,2,3,3\: things \: respectively$

$\implies i )Let \: us \: select \: first \: 2 \: things \\from \: 12 = ^{12}C{2}$

$Now, ii )2 \: more \: from \: remaining \: 10 \\= ^{10}C{2}$

$iii )2 \: more \: from \: remaining \: 8 \\= ^{8}C{2}$

$iv) 3 \: more \: from \: remaining \: 6 \\= ^{6}C{3}$

$v )3 \: more \: from \: remaining \: 3 \\= ^{3}C{3}$

$\red{ Number \: of \:ways } \\= ^{12}C{2}\times ^{10}C{2}\times ^{8}C{2} \times ^{6}C{3} \times ^{3}C{3}\\=66 \times 45 \times 28 \times 20 \times 1 \\= 1663200$

Therefore.,

$\red{ Number \: of \:ways }\green {= 1663200 }$

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