Question

Dante is arranging 11 cans of food in a row on a shelf. He has 7 cans of beans, 3 cans of peas, and 1 can of carrots. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?

Answer 1

Given:

The number of cans of food =11

The number of cans of beans=7

the number of cans of peas=3

the number of cans of carrots=1

Condition : two cans of the same food are considered identical.

To arrange the n objects in order,

`\begin{gathered} \text{Number of ways= }(n!)/(r_1!r_2!r_3!) \\ =(11!)/(7!3!1!) \\ =(39916800)/(30240) \\ =1320 \end{gathered}`

Answer: the number of ways are 1320.