5 letters are selected at random from the 9 letters in the word CELESTIAL. Find the number of different selections if the 5 letters include at least one $$\(\mathrm{E}\)$$ and at most one L. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_53 Year：2020 Question No：7(d)
Answer:
Scenarios are:
\[
\begin{array}{lll}
\mathrm{E} \mathrm{L}---{ }^{5} \mathrm{C}_{3} & 10 \\
\mathrm{E} \mathrm{L}-- & { }^{5} \mathrm{C}_{2} & 10 \\
\mathrm{E}---- & { }^{5} \mathrm{C}_{4} & 5 \\
\mathrm{E} \overline{\mathrm{E}}--- & { }^{5} \mathrm{C}_{3} & 10
\end{array}
\]
Summing the number of ways for 3 or 4 correct scenarios
$
\text { Total }=35
$
\[
\begin{array}{lll}
\mathrm{E} \mathrm{L}---{ }^{5} \mathrm{C}_{3} & 10 \\
\mathrm{E} \mathrm{L}-- & { }^{5} \mathrm{C}_{2} & 10 \\
\mathrm{E}---- & { }^{5} \mathrm{C}_{4} & 5 \\
\mathrm{E} \overline{\mathrm{E}}--- & { }^{5} \mathrm{C}_{3} & 10
\end{array}
\]
Summing the number of ways for 3 or 4 correct scenarios
$
\text { Total }=35
$
Knowledge points:
5.2.1 understand the terms permutation and combination, and solve simple problems involving selections
Solution:
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