Question

suppose that you bought 3 apple, 4 orange, and 2 fig trees. in how many different ways can these trees be planted in a row?

Answer 1

In 1260 different ways these trees can be planted in a row.

The selection of objects for their arrangement in a particular order is known as permutation. In permutation, the arrangement order of the selected items is also considered. Permutation can be known as an ordered combination. The selection of items from a collection where the order of the selection is neglected is known as a combination. The formula for permutations is

                                  ⇒ P(n,r) = n! / (n-r)!

Permutations are classified into three types- permutations of n different objects, permutations with repetition and permutations of multiple sets.

When we have 'n' different objects where $P_{1}, P_{2}$ and $P_{3}$ among 'n' objects are similar, then the permutations of multiple sets can be given by the formula,

                                  ⇒  $P = n! / p_{1}! . p_{2}! .....p_{k}!$       → 1

   where,        n = total number of objects

                      $p_{1} , p_{2}, .....p_{k}$ = objects in each individual sets

From the given problem,     n = 3(apple) + 4(orange) + 2(fig)

                                              n = 9

                                  $p_{1}$ = 3, $p_{2}$ = 4 and $p_{3}$ = 2

                                  ⇒   P =  9! / 3! . 4! . 2!

                                            =  362880 / 6 . 24 . 2

                                            =  362880 / 288

                                            =  1260

Therefore, we can plant trees in 1260 ways.

To know more about permutations (selections) refer to:

https://brainly.com/question/28443757

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