Question

A person always prefers to eat paratha and vegetable dishes in his meal . How many ways can he make his plate in a marriage party if there are three types of parathas, four types of vegetable dishes, three types of salads, and two types of sauces ?
$\begin{aligned} & A.3360 \\\ & B.4096 \\\ & C.3000 \\\ & D.\,None\,of\,these \\\ \end{aligned}$

Answer 1

For this question, first we have to find how many ways that the person can take paratha, then vegetable dishes, number of ways of salads and at last number of ways of sauces. And multiply all numbers.

Complete step by step solution:
To solve this question, first we have to number of ways he can choose or select one paratha is ${{2}^{3}}-1=7$
Next, the number of ways that he can select at least one vegetable dish is ${{2}^{4}}-1=15$
Now , the number of ways that he can select zero or more items from salads and sauces is ${{2}^{5}}=32$.
Because he prefers to eat paratha and vegetables for his meal, then at least he will take one paratha and one vegetable.
There is nothing mentioned about salad and sauce in the question, it means either he wants to take or not. That's why we combine it.
Hence the total number of ways that he can make his plate is $7\times 15\times 32=3360$.

Hence option A is the correct option.

Note:
Some students are always confused between Permutation and Combination, where, how and in which type of question we will apply Permutation concept or Combination.
Use permutation, if a problem calls the number of arrangements of objects and different order to be counted. Keep in mind that the given question is related to permutation.