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Let $\mathrm{P}=\left\{\mathrm{p}_{1}, \mathrm{p}_{2}, \mathrm{p}_{3}, \mathrm{p}_{4}\right\}$
$Q=\left\{q_{1}, q_{2}, q_{3}, q_{4}\right\}$ and
If $\begin{aligned} \mathrm{R}=\left\{\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}, \mathrm{r}_{4}\right\} \\ 10 &=\left\{\left(\mathrm{p}_{i}, \mathrm{q}_{\mathrm{f}}, \mathrm{r}_{\mathrm{k}}\right): \mathrm{i}+\mathrm{j}+\mathrm{k}=10\right\} \end{aligned}$
how many elements does $\mathrm{S}_{10}$ have?
Options:
$Q=\left\{q_{1}, q_{2}, q_{3}, q_{4}\right\}$ and
If $\begin{aligned} \mathrm{R}=\left\{\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}, \mathrm{r}_{4}\right\} \\ 10 &=\left\{\left(\mathrm{p}_{i}, \mathrm{q}_{\mathrm{f}}, \mathrm{r}_{\mathrm{k}}\right): \mathrm{i}+\mathrm{j}+\mathrm{k}=10\right\} \end{aligned}$
how many elements does $\mathrm{S}_{10}$ have?
Solution:
1219 Upvotes
Verified Answer
The correct answer is:
4
Given that $\mathrm{P}=\left\{\mathrm{p}_{1}, \mathrm{p}_{2}, \mathrm{p}_{3}, \mathrm{p}_{4}\right\}$
$Q=\left\{q_{1}, q_{2}, q_{3}, q_{4}\right\}$
and $\mathrm{R}=\left\{\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}, \mathrm{r}_{4}\right\}$
$\mathrm{S}_{10}=\left\{\mathrm{p}_{2}, \mathrm{q}_{4}, \mathrm{r}_{4}\right),\left(\mathrm{p}_{3}, \mathrm{q}_{3}, \mathrm{r}_{4}\right),\left(\mathrm{p}_{3}, \mathrm{q}_{4}, \mathrm{r}_{3}\right)$
$\left(\mathrm{p}_{4}, \mathrm{q}_{2}, \mathrm{r}_{4}\right)$
$\left.\left(\mathrm{p}_{4}, \mathrm{q}_{3}, \mathrm{r}_{3}\right),\left(\mathrm{p}_{4}, \mathrm{q}_{4}, \mathrm{r}_{2}\right)\right\}$
Total number of elements in $\mathrm{S}_{10}$ are 6 .
$Q=\left\{q_{1}, q_{2}, q_{3}, q_{4}\right\}$
and $\mathrm{R}=\left\{\mathrm{r}_{1}, \mathrm{r}_{2}, \mathrm{r}_{3}, \mathrm{r}_{4}\right\}$
$\mathrm{S}_{10}=\left\{\mathrm{p}_{2}, \mathrm{q}_{4}, \mathrm{r}_{4}\right),\left(\mathrm{p}_{3}, \mathrm{q}_{3}, \mathrm{r}_{4}\right),\left(\mathrm{p}_{3}, \mathrm{q}_{4}, \mathrm{r}_{3}\right)$
$\left(\mathrm{p}_{4}, \mathrm{q}_{2}, \mathrm{r}_{4}\right)$
$\left.\left(\mathrm{p}_{4}, \mathrm{q}_{3}, \mathrm{r}_{3}\right),\left(\mathrm{p}_{4}, \mathrm{q}_{4}, \mathrm{r}_{2}\right)\right\}$
Total number of elements in $\mathrm{S}_{10}$ are 6 .
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