Write in terms of factorial:5 × 10 × 15 × 20 × 25 - Mathematics and Statistics

Write in terms of factorial:
5 × 10 × 15 × 20 × 25

Sum

5 × 10 × 15 × 20 × 25
= (5 × 1) × (5 × 2) × (5 × 3) × (5 × 4) × (5 × 5)
= (5⁵) (5 × 4 × 3 × 2 × 1)
= (5⁵) (5!)

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Concept of Factorial Function

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Chapter 6: Permutations and Combinations - Exercise 6.2 [Page 75]

Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 4. (iv) | Page 75

Evaluate: 8!

Evaluate: 8! – 6!

Compute: `(12!)/(6!)`

Compute: 3! × 2!

Compute: `(8!)/(6! - 4!)`

Compute: `(8!)/((6 - 4)!)`

Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 8, r = 6

Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 12, r = 12

Find n, if (n + 3)! = 110 × (n + 1)!

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

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

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

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

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

A student passes an examination if he/she secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.

How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficient if a coefficient can be repeated in an equation.

A question paper has 6 questions. How many ways does a student have if he wants to solve at least one question?