Question:medium
If for \( 3 \leq r \leq 30 \), \( ^{30}C_{30-r} + 3 \left( ^{30}C_{31-r} \right) + 3 \left( ^{30}C_{32-r} \right) + ^{30}C_{33-r} = ^m C_r \), then \( m \) equals to_________
If for \( 3 \leq r \leq 30 \), \( ^{30}C_{30-r} + 3 \left( ^{30}C_{31-r} \right) + 3 \left( ^{30}C_{32-r} \right) + ^{30}C_{33-r} = ^m C_r \), then \( m \) equals to_________
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Whenever you see coefficients like 1, 2, 1 or 1, 3, 3, 1 in a combination sum, it indicates that Pascal's identity is being applied 2 or 3 times respectively. The upper index \( n \) will increase by the power of the expansion.
Updated On: Apr 2, 2026
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Correct Answer: 33
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