(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

(ii) There are 3 types of toy car and 2 types of toy train available in a shop. Find the

Question

(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

(ii) There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?

(iii) How many two-digit numbers can be formed using $1,2,3,4,5$ without repetition of digits?

(iv) Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?

(v) In how many ways 5 persons can be seated in a row?

Accepted Answer

> [!TLDR]
>
> Each part is a direct application of the Sum Rule, the Product Rule, or the arrangement formulas $^nP_r=\dfrac{n!}{(n-r)!}$ and $n!$.

**Step 1. (i)** Selecting **either** an Indian **or** a Chinese item are non-simultaneous alternatives, so by the Sum Rule: $10+7=17$ ways.

**Step 2. (ii)** Buying a car **and** a train are two independent procedures done together, so by the Product Rule: $3	imes2=6$ ways.

**Step 3. (iii)** A two-digit number from $\{1,2,3,4,5\}$ without repetition: tens place has $5$ choices, units place has $4$ remaining choices $\Rightarrow 5	imes4={}^5P_2=20$.

**Step 4. (iv)** $3$ persons taking $3$ of the $10$ distinct seats (order matters — which seat each person takes): $^{10}P_3=10	imes9	imes8=720$.

**Step 5. (v)** $5$ persons seated in a row (all $5$ arranged): $5!=120$.
> [!ANSWER]
> (i) $17$  (ii) $6$  (iii) $20$  (iv) $720$  (v) $120$.

Q.(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

Concept understanding — Fundamental Principles of Counting

The Fundamental Principle of Counting

The Intuition: A Fork in the Road

The Precise Statement

A Simple Example

Why This Matters

Q.(i) A person went to a restaurant for dinner. In the menu card, the person saw 10 Indian and 7 Chinese food items. In how many ways the person can select either an Indian or a Chinese food?

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