Question

Ajutati-ma va rog sa rezolv ))

Answer 1

Folosesti formulele:

$n!=1\cdot2\cdot3\cdot...\cdot n$

$A_n^k=n\cdot(n-1)\cdot(n-2)\cdot...\cdot(n-k+1)$ aici este bine sa retii ca sunt exact k factori.

$C_n^k=\dfrac{A_n^k}{P_k}$

$P_n=n!$

Answer 2

$a) \, \, \frac{A_5^4}{P_4} = \frac{5*4*3*2}{1*2*3*4}=5 \\ \\ b)\, \, {A_7^5}*{C_5^3}= (7*6*5*4*3)*\frac{5*4*3}{1*2*3}= \\ = (7*6*5*4*3) * 10 = 2520*10 =25200 \\ \\ c)\, \, \frac{C_7^4}{P_6}= \frac{7*6*5*4}{(1*2*3*4)*(1*2*3*4*5*6)} = \frac{5}{1*2*3*4*5*6}= \frac{1}{1*2*3*4*6}$