Question

If there are seven nouns 5 verbs and 2 adjectives how many ways are there to form a sentence by choosing one word of each type

Answer 1

Let
`n_1,n_2,\ldots, n_7` be the seven nouns,
`v_1,v_2,\ldots, v_5` be the five verbs, and
`a_1, a_2` be the two adjective.

You want to form a sentence of the following form:

`n_i\ \ v_j\ \ a_k,\quad i \in \{1,2,\ldots, 7\},\ j \in \{1,2,3,4,5\},\ k \in \{1,2\}`

So, let's start with the choice of the noun. We have seven choice since there are seven nouns in total.

Once we made the first choice, it's time the verb. For each of the seven choice we had for the noun, we have 5 choice for the verbs. This leads to 35 possible combinations of nouns and verbs.

Finally, for each of the 35 choices we had so far, we have to make the last choice: adjective1 or adjective 2? This means that the 35 choices bisect again, leading to a total of 70 possible sentences.