Respuesta :
Answer:
A) The probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding 30
Solution: Total integers = 30
No. of integers to be selected = 6
So, The no. of possible ways of selecting 6 integer out of 30 = [tex]^{30}C_6[/tex]
So, The probability of winning a lottery by selecting the correct six integers :
= [tex]\frac{1}{^{30}C_6}[/tex]
= [tex]\frac{1}{593775}[/tex]
B)The probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding 36
Solution: Total integers = 36
No. of integers to be selected = 6
So, The no. of possible ways of selecting 6 integer out of 36 = [tex]^{36}C_6[/tex]
So, The probability of winning a lottery by selecting the correct six integers :
= [tex]\frac{1}{^{36}C_6}[/tex]
= [tex]\frac{1}{1947792}[/tex]
C)The probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding 42
Solution: Total integers = 42
No. of integers to be selected = 6
So, The no. of possible ways of selecting 6 integer out of 42 = [tex]^{42}C_6[/tex]
So, The probability of winning a lottery by selecting the correct six integers :
= [tex]\frac{1}{^{42}C_6}[/tex]
= [tex]\frac{1}{5245786}[/tex]
D)The probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding 48
Solution: Total integers = 48
No. of integers to be selected = 6
So, The no. of possible ways of selecting 6 integer out of 48 = [tex]^{48}C_6[/tex]
So, The probability of winning a lottery by selecting the correct six integers :
= [tex]\frac{1}{^{48}C_6}[/tex]
= [tex]\frac{1}{12271512}[/tex]
