CUET PG 2021 — Mathematics PYQ

1. Har dost ke liye choices:

   Kyunki har dost ke paas 2 options hain, toh 6 doston ke liye total combinations honge:

   $$2\times 2\times 2\times 2\times 2\times 2=2^6$$

2. Condition: "One or more" (Ek ya ek se zyada):

   $2^6$ mein wo saare cases shamil hain jahan 1 dost aata hai, 2 aate hain... aur wo case bhi shamil hai jahan koi bhi nahi aata.

   Lekin sawal mein likha hai ki kam se kam ek dost ko bulana zaroori hai. Iska matlab humein wo 1 case minus karna hoga jisme kisi ko nahi bulaya gaya ($0$ friends invited).

3. Final Calculation:

   Total ways ka formula hoga:

   $$2^n-1$$

   Yahan $n=6$ hai.

   $$2^6-1$$
   $$64-1=63$$

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Alternative Method (Combinations):

Aap ise aise bhi soch sakte hain:

• 6 mein se 1 dost ko bulane ke tarike: ${}^6{C}_1$

• 6 mein se 2 doston ko bulane ke tarike: ${}^6{C}_2$

  ...aur aise hi 6 tak.