Permutation and Combination
Permutation and Combination
Allen Star Batch
Grade 11
Question:
Seven different coins are to be divided amongst three persons. If no two of the persons receive the same number of coins but each receives atleast one coin & none is left over, then the number of ways it which the division may be made is:
420
630
710
None of these
Step-by-Step Solution
Key Concept: Comparing consecutive binomial coefficients using the ratio test $\frac{C_r}{C_{r-1}}$ determines where terms increase and where they decrease.
To find when $T_{r+1} > T_r$ in the binomial expansion, we compare $^{24}C_r x^{24}$ and $^{24}C_{r-1}x^{r-1}$. Setting $\frac{^{24}C_r}{^{24}C_{r-1}} > 1$ gives $\frac{25-r}{r} > 1$, so $r T_r$, confirming the maximum term occurs at $r = 12$.
Correct Answer: 2