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The symbol ₁₂P₉ represents the permutations of 9 quantities out of 12.
By definition,

From the calculator,
12! = 479,001,600
3! = 6
Therefore
₁₂P₉ = 479001600/6 = 79,833,600
Answer: 79,833,600
Answer:
<u>The present age of the mother is 30 years old</u>
Step-by-step explanation:
Age of Jane = x
Age of Billy = 5x (Billy is five times as old as Jane)
Age of Sara = 15x (Their mother is now three times as old as Billy)
In 2 years Sara will be eight times as old as Jane, therefore:
15x + 2 = 8 (x + 2)
15x + 2 = 8x + 16
15x - 8x = 16 - 2
7x = 14
x = 14/7
x = 2 ⇒ 5x = 10x ⇒ 15x = 30
Jane's present age is 2, Billy's present age is 10 and Sara's present age is 30
<u>The present age of the mother is 30 years old</u>