QUESTION या शब्दामधून 5 मूळाक्षरांची अशी निवड करावयाची आहे की, ज्यात कमीत कमी 2 स्वरांचा समावेश असेल आणि कोणत्याही मूळाक्षराची पुनरावृत्ती झालेली नसेल, तर अशी निवड किती प्रकारे करता येईल ते शोधा.

The correct answer is Option D (52).

Key Points:
• Combinations Formula & Step-by-Step Calculation:
• The word QUESTION has 8 distinct letters:
• Vowels (4): E, U, I, O
• Consonants (4): Q, S, T, N
• We need to choose 5 letters such that there are at least 2 vowels.
• Total ways to choose any 5 letters from 8 = binom85 = (8 × 7 × 6)/(3 × 2 × 1) = 56.
• Cases violating 'at least 2 vowels':
• 1. 0 vowels (5 consonants): Not possible since there are only 4 consonants (0 ways).
• 2. Exactly 1 vowel and 4 consonants:
• Ways = binom41 × binom44 = 4 × 1 = 4.
• Total favorable combinations = Total - (Cases with < 2 vowels) = 56 - 4 = 52.
• Or by direct addition:
• 2 Vowels, 3 Consonants: binom42 × binom43 = 6 × 4 = 24
• 3 Vowels, 2 Consonants: binom43 × binom42 = 4 × 6 = 24
• 4 Vowels, 1 Consonant: binom44 × binom41 = 1 × 4 = 4
• Sum = 24 + 24 + 4 = 52.
• Hence, there are 52 ways.
• Key Takeaway: Total selections binom85 = 56 minus 1-vowel case binom41 × binom44 = 4 leaves 52 valid combinations.