The total number of ways of selecting six coi | vedclass

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Question

(A) The problem asks for the number of ways to select $6$ coins from $3$ distinct types of coins (one-rupee,fifty-paise,and twenty-five-paise). Since

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(A) The problem asks for the number of ways to select $6$ coins from $3$ distinct types of coins (one-rupee,fifty-paise,and twenty-five-paise). Since the number of coins of each type $(20, 10, 7)$ is greater than or equal to the number of coins to be selected $(6)$,we can treat this as a selection with repetition allowed. The number of ways to select $r$ items from $n$ types of items with repetition is given by the formula $^{n+r-1}C_r$. Here,$n = 3$ (types of coins) and $r = 6$ (number of coins to select). Substituting these values into the formula: Number of ways $= ^{3+6-1}C_6 = ^8C_6$. Using the property $^nC_r = ^nC_{n-r}$,we have $^8C_6 = ^8C_2$. $^8C_2 = \frac{8 	imes 7}{2 	imes 1} = 28$. Thus,the total number of ways is $28$.

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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