যদি ⁿP_r = 336 এবং ⁿC_r = 56 হয়, তবে n=?

Explanation:

Another Explanation (5): দেওয়া আছে, ⁿP_r = 336 এবং ⁿC_r = 56 আমরা জানি, ⁿP_r = \(\frac{n!}{(n-r)!}\) এবং ⁿC_r = \(\frac{n!}{r!(n-r)!}\) সুতরাং, \(\frac{^{n}P_{r}}{^{n}C_{r}} = \frac{\frac{n!}{(n-r)!}}{\frac{n!}{r!(n-r)!}} = \frac{n!}{(n-r)!} \times \frac{r!(n-r)!}{n!} = r!\) এখন, \(\frac{^{n}P_{r}}{^{n}C_{r}} = \frac{336}{56}\) \(r! = 6\) 😲 \(r! = 3 \times 2 \times 1 = 3!\) সুতরাং, r = 3 🤔 আমরা জানি, ⁿC_r = \(\frac{n!}{r!(n-r)!}\) ⁿC₃ = 56 \(\frac{n!}{3!(n-3)!} = 56\) \(\frac{n(n-1)(n-2)(n-3)!}{3!(n-3)!} = 56\) \(\frac{n(n-1)(n-2)}{3!} = 56\) \(n(n-1)(n-2) = 56 \times 3! = 56 \times 6 = 336\) এখন, \(n(n-1)(n-2) = 8 \times 7 \times 6\) 🤩 সুতরাং, n = 8 🥳