MATH SOLVE

3 months ago

Q:
# In a lottery game, a player picks six numbers from 1 to 48. If 4 of those 6 numbers match those drawn, the player wins third prize. What is the probability of winning this prize?

Accepted Solution

A:

[tex]|\Omega|={_{48}C_6}=\dfrac{48!}{6!42!}=\dfrac{43\cdot44\cdot45\cdot46\cdot47\cdot48}{720}=12271512\\|A|={_6C_4}=\dfrac{6!}{4!2!}=\dfrac{5\cdot6}{2}=15\\\\P(A)=\dfrac{15}{12271512}=\dfrac{5}{4090504}\approx1.2\%[/tex]