# Please solve part (2)

there are 5 position

in committee a particular official member is never included therefore number of official members left for the position = 8-1=7

number of non official members =4

total number of members left for position =11

now out of 11 members only 5 members can be selected

therefore number different committee =

^{11}C

_{5 }=

$=\frac{11!}{5!(11-5)!}\phantom{\rule{0ex}{0ex}}=\frac{11!}{5!6!}\phantom{\rule{0ex}{0ex}}=\frac{11\times 10\times 9\times 8\times 7\times 6!}{5!6!}\phantom{\rule{0ex}{0ex}}=\frac{11\times 10\times 9\times 8\times 7}{5!}=462$

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