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Convert into factorials : 2.4.6.8.10....

Convert into factorials :
2.4.6.8.10.12……..50

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To convert the product \( 2 \times 4 \times 6 \times 8 \times 10 \times 12 \ldots \times 50 \) into factorials, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Pattern**: The given sequence consists of even numbers from 2 to 50. We can express each even number in terms of its position in the sequence. The \( n \)-th even number can be expressed as \( 2n \). 2. **List the Even Numbers**: The even numbers from 2 to 50 can be represented as: \[ ...
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AAKASH INSTITUTE ENGLISH-PERMUTATIONS AND COMBINATIONS -Try Yourself
  1. Evaluate : (1)/(3!)+(1)/(4!)+(1)/(5!)

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  2. Convert into factorials 3.6.9.12.15.18.21

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  3. Convert into factorials : 2.4.6.8.10.12……..50

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  4. Evaluate : (n!)/((n-r)!) where n=5,r=2

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  5. Evaluate (n!)/(r!(n-r)!), where n=15,r=4

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  6. Evaluate ""^(20)P(3)

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  7. Evaluate ""^(5)P(3)xx""^(7)P(3)

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  8. Find n, if ""^(n)P(5)=42 ""^(n)P(3), n ge 5

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  9. Show that ""^(n)P(n)=2""^(n)P(n-2)

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  10. In how many ways, the letter of word NUMBER can be arranged ?

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  11. In how many ways, the letters of word FRACTION can be arranged ?

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  12. How many numbers lying between 100 and 1000 can be formed with the dig...

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  13. How many four digit numbers are there in all?

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  14. How many permulations of the letters of the word KARNAL are there ?

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  15. How many words can be formed using the letters E twice , the letter C ...

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  16. Find the number of words formed by permuting all letters of the word I...

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  17. Find the number of different words formed with the letters of the word...

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  18. How many permutations can be made out of the letters of the word TRIAN...

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  19. Find out number of permutations that can be had from the letters of th...

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  20. How many numbers greater than 50,000 can be formed by using the digits...

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