Moderate -0.8 This is a straightforward permutations question testing standard formulas for arrangements with repetition (7!/(3!×2!)) and combinations (product of binomial coefficients). Part (ii) requires basic probability calculation. All techniques are routine textbook exercises requiring only formula recall and arithmetic, making this easier than average for A-level.
The diagram shows 7 cards, each with a digit printed on it. The digits form a 7 -digit number.
1
3
3
3
5
5
9
How many different 7 -digit numbers can be formed using these cards?
The diagram below shows 5 white cards and 10 grey cards, each with a letter printed on it.
\includegraphics[max width=\textwidth, alt={}, center]{98ac515d-fd47-4864-afd6-321e9848d6cb-04_398_801_596_632}
From these cards, 3 white cards and 4 grey cards are selected at random without regard to order.
How many selections of seven cards are possible?
Find the probability that the seven cards include exactly one card showing the letter A .
6 (i) The diagram shows 7 cards, each with a digit printed on it. The digits form a 7 -digit number.
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | }
\hline
1 & 3 & 3 & 3 & 5 & 5 & 9 \\
\hline
\end{tabular}
\end{center}
How many different 7 -digit numbers can be formed using these cards?\\
(ii) The diagram below shows 5 white cards and 10 grey cards, each with a letter printed on it.\\
\includegraphics[max width=\textwidth, alt={}, center]{98ac515d-fd47-4864-afd6-321e9848d6cb-04_398_801_596_632}
From these cards, 3 white cards and 4 grey cards are selected at random without regard to order.
\begin{enumerate}[label=(\alph*)]
\item How many selections of seven cards are possible?
\item Find the probability that the seven cards include exactly one card showing the letter A .
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2011 Q6 [10]}}