5Question: A research team at the NIH reviews 120 grant applications, of which 45 focus on cancer research, 50 on neuroscience, and 25 on infectious diseases. If three applications are selected at random without replacement, what is the probability that all three selected apply to different fields? - Treasure Valley Movers
5Question: A research team at the NIH reviews 120 grant applications, of which 45 focus on cancer research, 50 on neuroscience, and 25 on infectious diseases. If three applications are selected at random without replacement, what is the probability that all three selected apply to different fields?
5Question: A research team at the NIH reviews 120 grant applications, of which 45 focus on cancer research, 50 on neuroscience, and 25 on infectious diseases. If three applications are selected at random without replacement, what is the probability that all three selected apply to different fields?
Curious about patterns behind NIH funding choices? A recent review by a research team examined 120 grant proposals, revealing a balanced yet priority-driven distribution across key biomedical areas: 45 cancer-focused, 50 neuroscience, and 25 infectious disease projects. This mix reflects growing national interest in cutting-edge health research—especially in brain function and infectious disease resilience—while supporting life-saving cancer advances. With such diverse investment, understanding how likely it is that three randomly chosen grants span all major disciplines adds context to public and scientific discourse.
Understanding the Likelihood of Diverse Selection
The core question explores the probability that three randomly selected grant applications—chosen without bias and without replacement—represent distinct fields: cancer, neuroscience, and infectious diseases. This doesn’t require predicting individual grants but relies on combinatorial math grounded in real data.
Understanding the Context
The total number of ways to choose any three applications from 120 is given by the combination formula:
120 choose 3 = 120! / (3! × 117!) = (120 × 119 × 118) / 6 = 285,640
To yield three with different fields, the selection must include one from each category. Since there are 45 in cancer, 50 in neuroscience, and 25 in infectious diseases, the number of favorable combinations is the product:
45 × 50 × 25 = 56,250
Thus, the probability is:
**56,250 / 285,640 ≈ 0.1972, or about
