Expand \(( 2 + x ) ^ { - 2 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), and state the set of values of \(x\) for which the expansion is valid.
Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(\frac { 1 + x ^ { 2 } } { ( 2 + x ) ^ { 2 } }\). [0pt]
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\section*{6.}
The diagram below shows 5 white cards and 10 grey cards, each with a letter printed on it.
\includegraphics[max width=\textwidth, alt={}, center]{d193321f-0471-48cd-b954-4a7330777491-14_424_849_287_520}
From these cards, 3 white cards and 4 grey cards are selected at random without regard to order.
(a) How many selections of seven cards are possible?
(b) Find the probability that the seven cards include exactly one card showing the letter A . [0pt]
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