The total number of ways of selecting six coins out of 20 one-rupee coins, 10 fifty- paise coins, and 7 twenty-five paise coins is:

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Solution

Using multinomial theorem, we have
$x_{1} + x_{2} + x_{3} = 6$ where $0 \leq x_{1} \leq 6$ $0 \leq x_{2} \leq 0$ $0 \leq x_{3} \leq 0$
$\Rightarrow$ Total no. of ways is $^{n + r - 1} C_{r}$
$=^{3 + 6 - 1} C_{6} =^{8} C_{6}$
$= 28$

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The total number of ways of selecting six coins out of 20 one-rupee coins, 10 fifty- paise coins, and 7 twenty-five paise coins is:

Using multinomial theorem, we havex1+x2+x3=6 where 0≤x1≤6 0≤x2≤0 0≤x3≤0⇒ Total no. of ways is n+r−1Cr=3+6−1C6=8C6=28

Using multinomial theorem, we have
$x_{1} + x_{2} + x_{3} = 6$ where $0 \leq x_{1} \leq 6$ $0 \leq x_{2} \leq 0$ $0 \leq x_{3} \leq 0$
$\Rightarrow$ Total no. of ways is $^{n + r - 1} C_{r}$
$=^{3 + 6 - 1} C_{6} =^{8} C_{6}$
$= 28$