In a shop,there are 5 types of ice-creams ava | vedclass

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

Question

(D) This is a problem of combinations with repetition allowed (multiset coefficient). The number of ways to choose $r$ items from $n$ types with repet

Vedclass · Accepted Answer

Statement-$1$ is false,Statement-$2$ is true.

Vedclass · Answer

(D) This is a problem of combinations with repetition allowed (multiset coefficient). The number of ways to choose $r$ items from $n$ types with repetition is given by the formula $^{n+r-1}C_r$. Here,$n = 5$ (types of ice-creams) and $r = 6$ (ice-creams to be bought). Number of ways = $^{5+6-1}C_6 = ^{10}C_6$. Since $^{10}C_6 = ^{10}C_{10-6} = ^{10}C_4$,Statement-$1$ is false because it states $^{10}C_5$. For Statement-$2$,the number of ways to arrange $6$ $A$'s and $4$ $B$'s is given by the permutation of multisets formula: $\frac{(6+4)!}{6!4!} = ^{10}C_6$. Since the number of ways to buy the ice-creams is $^{10}C_6$ and the number of arrangements is also $^{10}C_6$,Statement-$2$ is true. Therefore,Statement-$1$ is false and Statement-$2$ is true.

Similar Questions

$A$ person wants to climb a $n$-step staircase using one step or two steps. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

The number of different words that can be formed from the letters of the word $SUCCESS$ in which the two $C$ are together but no two $S$ are together are:

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

In an election,there are $5$ candidates and $3$ vacancies. $A$ voter can vote for a maximum of $3$ candidates. In how many ways can a voter cast their vote?

Vedclass Test Series

Exam Paper Generator

Online Exam Module