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# Combinatorics and Integers | TOMATO B.Stat Objective 93

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective based on Combinatorics and Integers. You may use sequential hints to solve the problem.

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Combinatorics and Integers.

## Combinatorics and Integers (B.Stat Objective Question)

The highest power of 18 contained in $${50 \choose 25}$$ is

• 104
• 1
• 1154
• none of these

### Key Concepts

Integers

Combinatorics

Exponents

But try the problem first…

Source

B.Stat Objective Problem 93

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

here $${50 \choose 25}$$=$$\frac{50!}{(25!)^{2}}$$=$$\frac{(50)(49)(….)(26)}{(25)(24)(…)(1)}$$

Second Hint

$$=(2)^{13}(49)(47)(45)(43)(41)(39)(37)(35)(33)(31)(29)(27) \times \frac{1}{12!}$$

Final Step

$$=(2)^{10}(49)(47)(15)(43)(41)(13)(37)(35)(11)(31)(29)\times \frac{1}{(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}[(2)^{3}(27)(9)(3)]$$

$$=(2)^{10}(49)(47)(15)(43)(41)(13)(37)(35)(11)(31)(29)\times \frac{1}{(12)(11)(10)(8)(7)(5)(4)(1)}[(2)(9)]$$gives a factor of $$(18)^{1}$$ then highest power of 18 is 1.

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