The total number of ways of selecting six coi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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:

Similar Questions

$A = \{ x_1, x_2, x_3, x_4 \}; \, B = \{ y_1, y_2, y_3, y_4 \}.$ $A$ function is defined from set $A$ to set $B.$ The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

In how many ways can $6$ apples be distributed among $3$ boys,there being no restriction to the number of apples each boy may get?

If $^{2n}C_2 : ^nC_2 = 9:2$ and $^nC_r = 10$,then $r = $

The sum $\sum_{r=1}^{10} (r^2 + 1) \times (r!)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module