Find the total number of different arrangements of the 11 letters in the word CATERPILLAR that contain both Rs and at least one A and at least one L. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m21_qp_52 Year：2021 Question No：6(c)
Answer:
Method 1
\( \begin{array}{lll}\operatorname{RRA} \mathrm{R} & { }^{5} \mathrm{C}_{2} & =10 \\ \operatorname{RRA} \overline{\mathrm{L}}- & { }^{5} \mathrm{C}_{1} & =5 \\ \operatorname{RRA} \mathrm{R} \mathrm{L} & { }^{5} \mathrm{C}_{1} & =5 \\ \operatorname{RRAA} \overline{\mathrm{L}} & & =1\end{array} \)
\( [Total =] 21 \)
Method 2 - Fixing RRAL first.
N.B. No other scenarios can be present anywhere in solution.
\( \mathrm{RRAL} \wedge \wedge{ }^{7} \mathrm{C}_{2} \)
\( [ Total =] 21 \)
\( \begin{array}{lll}\operatorname{RRA} \mathrm{R} & { }^{5} \mathrm{C}_{2} & =10 \\ \operatorname{RRA} \overline{\mathrm{L}}- & { }^{5} \mathrm{C}_{1} & =5 \\ \operatorname{RRA} \mathrm{R} \mathrm{L} & { }^{5} \mathrm{C}_{1} & =5 \\ \operatorname{RRAA} \overline{\mathrm{L}} & & =1\end{array} \)
\( [Total =] 21 \)
Method 2 - Fixing RRAL first.
N.B. No other scenarios can be present anywhere in solution.
\( \mathrm{RRAL} \wedge \wedge{ }^{7} \mathrm{C}_{2} \)
\( [ Total =] 21 \)
Knowledge points:
5.2.1 understand the terms permutation and combination, and solve simple problems involving selections
Solution:
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