Permutations & Combinations
Selection problems
Grade 11
Question:
<p>A person always prefers to eat <em>parantha</em> and vegetable dish in his meal. How many ways can he make his platter in a marriage party if there are three types of paranthas, four types of vegetable dish, three types of salads, and two types of sauces?</p>
<p>3360</p>
<p>4096</p>
<p>3000</p>
<p>none of these</p>
Step-by-Step Solution
Key Concept: The person MUST choose exactly one parantha AND one vegetable dish (mandatory selections), while salads and sauces are optional. Apply the fundamental counting principle only to required items.
<p><strong>Step 1:</strong> Identify mandatory selections: The person must have exactly 1 parantha AND 1 vegetable dish.</p><p><strong>Step 2:</strong> Identify optional selections: Salads and sauces are not mandatory (the problem says he 'prefers' only parantha and vegetable).</p><p><strong>Step 3:</strong> Apply fundamental counting principle for mandatory items only:</p><p>Number of ways = (Ways to choose parantha) × (Ways to choose vegetable dish)</p><p>Number of ways = 3 × 4 = <strong>12</strong></p><p>∴ Answer: A</p>
Correct Answer: A