IPMAT Rohtak 2020 (QA) - How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time? | PYQs + Solutions | AfterBoards
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IPMAT Rohtak 2020

Modern Math
>
Permutation & Combination

Easy

How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Correct Option: 4
Since any number of symbols can be used:\newlineUsing 1 symbol: 6C1^6C_1 × 1P1=6×1^1P_1 = 6 × 1 ways\newlineUsing 2 symbols: 6C2^6C_2 × 2P2=15×2^2P_2 = 15 × 2 ways\newlineUsing 3 symbols: 6C3^6C_3 × 3P3=20×6^3P_3 = 20 × 6 ways\newlineUsing 4 symbols: 6C4^6C_4 × 4P4=15×24^4P_4 = 15 × 24 ways\newlineUsing 5 symbols: 6C5^6C_5 × 5P5=6×120^5P_5 = 6 × 120 ways\newlineUsing 6 symbols: 6C6^6C_6 × 6P6=1×720^6P_6 = 1 × 720 ways
Total = 6(1)+15(2)+20(6)+15(24)+6(120)+1(720)6(1) + 15(2) + 20(6) + 15(24) + 6(120) + 1(720)\newline= 6+30+120+360+720+7206 + 30 + 120 + 360 + 720 + 720\newline= 19561956
Therefore, 1956 different signposts can be made.

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