Permutations & Combinations
Restricted permutations with conditions
Grade 11
Question:
<p>Number of six digit numbers that can be formed using digits 1, 2, 3, 4, 5, 6 (each digit used exactly once) having the property that for each digit, not more than two digits smaller than that digit appear to the right of that digit, is:</p>
<p>(a) 120</p>
<p>(b) 144</p>
<p>(c) 162</p>
<p>(d) 210</p>
Step-by-Step Solution
Key Concept: Count permutations with the constraint that each element has at most 2 smaller elements to its right. This requires systematic enumeration or recursive counting.
<p>This is a counting problem with restricted permutations. We need to count permutations of 1, 2, 3, 4, 5, 6 where for each digit, at most 2 smaller digits appear to its right.</p><p>This is equivalent to counting permutations that avoid certain patterns. The number of such valid permutations is 162.</p>
Correct Answer: c