HSC Commerce: Marketing and Salesmanship 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!

Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12

Find n, if: `((2"n")!)/(7!(2"n" - 7)!) : ("n"!)/(4!("n" - 4)!)` = 24:1

Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`

Show that: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`

Find the value of: `(8! + 5(4!))/(4! - 12)`

Find the value of: `(5(26!) + (27!))/(4(27!) - 8(26!)`

Show that: `((2"n")!)/("n"!)` = 2ⁿ(2n – 1)(2n –  3)....5.3.1

Two dice are thrown together. What is the probability that sum of the numbers on two dice is 5 or number on the second die is greater than or equal to the number on the first die?

A card is drawn from a pack of 52 cards. What is the probability that, card is either red or black?

A card is drawn from a pack of 52 cards. What is the probability that card is either red or face card?

Two cards are drawn from a pack of 52 cards. What is the probability that, both the cards are of same colour?

A bag contains 50 tickets, numbered from 1 to 50. One ticket is drawn at random. What is the probability that, number on the ticket is a perfect square or divisible by 4?

A bag contains 50 tickets, numbered from 1 to 50. One ticket is drawn at random. What is the probability that, number on the ticket is a prime number or greater than 30?

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed in both. Find the probability that student selected at random passed in at least one examination.

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random passed in exactly one examination.

Hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that student selected at random failed in both the examinations.

If P(A) = `1/4`, `"P"("B") = 2/5` and `"P"("A" ∪ "B") = 1/2` Find the value of the following probability: P(A ∩ B)

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A ∩ B')