6 men and 4 women are ranked according to their scores on an exam. Assume that no two scores are alike, and that all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a man (so X=1 indicates that a man achieved the highest score on the exam).
a. Find P{X = i}, i=1, 2, 3, ..., 8, 9, 10.

The probability distribution table for X is attached below.

Step-by-step explanation:

Total number of students = 10

All the 10 students gets different ranks from the range 1 to 10.

Number of females = 4

Number of males = 6

The random variable X is defined as the highest ranking achieved by a man.

Total number of ways of ranking 10 different scores is: 10!

Number of ways a male can be ranked 1 is:

= (#ways of choosing any one male out of 6)

                           × (#ways of arranging the rest 9)

= (⁶C₁ × 9!)

Compute the value of P (X = 1) as follows:

Number of ways a male can be ranked 2 is:

= (#ways of choosing any one female out of 4)

                × (#ways of choosing any one male out of 6)

                           × (#ways of arranging the rest 8)

= (⁴C₁ × ⁶C₁ × 8!)

Compute the value of P (X = 2) as follows:

Number of ways a male can be ranked 3 is:

= (#ways of choosing two female out of 4)

                × (#ways of choosing any one male out of 6)

                           × (#ways of arranging the rest 7)

= (⁴C₂ × ⁶C₁ × 7!)

Compute the value of P (X = 3) as follows:

Number of ways a male can be ranked 4 is:

= (#ways of choosing three female out of 4)

                × (#ways of choosing any one male out of 6)

                           × (#ways of arranging the rest 6)

= (⁴C₃ × ⁶C₁ × 6!)

Compute the value of P (X = 4) as follows:

Number of ways a male can be ranked 5 is:

= (#ways of choosing four female out of 4)

                × (#ways of choosing any one male out of 6)

                           × (#ways of arranging the rest 5)

= (⁴C₄ × ⁶C₁ × 5!)

Compute the value of P (X = 5) as follows:

Since there are only 4 female students, the lowest value of X can be 5.

So the probabilities of X greater than 6 are 0.

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.