Permutation and Combination - Factorial - Solved Example - Find x 1/8! + 1/9! = x/10!

𝐏𝐞𝐫𝐦𝐮𝐭𝐚𝐭𝐢𝐨𝐧 𝐚𝐧𝐝 𝐂𝐨𝐦𝐛𝐢𝐧𝐚𝐭𝐢𝐨𝐧 - 𝐅𝐚𝐜𝐭𝐨𝐫𝐢𝐚𝐥 - 𝐒𝐨𝐥𝐯𝐞𝐝 𝐄𝐱𝐚𝐦𝐩𝐥𝐞𝐬
𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧:
Find x if x/10! = 1/8! + 1/9!
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
x/10! = 1/8! + 1/9!
∴ x/10! = (10 x 9) / [(10 x 9) x 8!] + 10 / 10 x 9!
∴ x/10! = (10 x 9) / 10! + 10 / 10!
∴ x/10! = (10 x 9) + 10 / 10!
∴ x/10! = (90 + 10) / 10!
∴ x/ ̶1̶0̶!̶ = (90 + 10) / ̶1̶0̶!̶
∴ x = (90 + 10)
∴ x = 100
𝐀𝐧𝐬𝐰𝐞𝐫:
x = 100 if x/10! = 1/8! + 1/9!

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𝐋𝐞𝐚𝐫𝐧𝐢𝐧𝐠 𝐎𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞:
✔️ What is Factorial?
✔️ What is n x (n - 1)!
𝐂𝐨𝐧𝐜𝐞𝐩𝐭:
✔️ The product of 'n' natural numbers is called factorial.
For example if we multiply first 5 natural numbers, we obtain 5 factorial and if we multiply first 10 natural numbers, we obtain 10 factorial.
✔️ Factorial is denoted as "!". So the product of n natural numbers is n! (read as n factorial).
For example 1 x 2 x 3 = n!
For example (Reverse Order) n x (n-1) x (n-2) x 3 x 2 x 1 = n!
For example 1 x 2 x 3 x 4 x 5 = 5!
For example (Reverse Order) 5 x 4 x 3 x 2 x 1 = 5!
For example 1 x 2 x 3 x 4 x 5 x 6 = 6!
For example (Reverse Order) 6 x 5 x 4 x 3 x 2 x 1 = 6!
𝐈𝐦𝐩𝐨𝐫𝐭𝐚𝐧𝐭 𝐟𝐚𝐜𝐭𝐨𝐫𝐢𝐚𝐥𝐬 𝐭𝐨 𝐫𝐞𝐦𝐞𝐦𝐛𝐞𝐫
6! = 720
5! = 120
4! = 24
3! = 6
2! = 2
1! = 1
0! = 1
𝐏𝐫𝐨𝐩𝐞𝐫𝐭𝐲 𝐨𝐟 𝐅𝐚𝐜𝐭𝐨𝐫𝐢𝐚𝐥𝐬
✔️ n x (n - 1)! = n!
For example if we multiply 5 with 4! [5 x 4!] or [5 x 4 x 3 x 2 x 1], we obtain 5!
For example if we multiply 6 with 5! [6 x 5!] or [6 x 5 x 4 x 3 x 2 x 1], we obtain 6!
𝐅𝐮𝐥𝐥 𝐏𝐥𝐚𝐲𝐥𝐢𝐬𝐭 𝐨𝐧 𝐅𝐚𝐜𝐭𝐨𝐫𝐢𝐚𝐥𝐬