$\"\"$ \ \

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The volunteer checks $\"\"$ canned goods per hour, so $\"\"$ .

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In one hour, how many different ways it is possible to open the chest and find gold coins exactly $\"\"$ times, so $\"\"$ .

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(a)

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Find the value of $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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The probability that a canned good received at a food bank is ditributed to the needy is $\"\"$ , so $\"\"$ .

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The value of $\"\"$ .

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Find the probability that a volunteer checking canned goods will find themselves throwing out itms less than $\"\"$ times, so $\"\"$ or $\"\"$ or $\"\"$ and $\"\"$ .

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Find the value of $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the probability to get less than $\"\"$ times is

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$\"\"$ or $\"\"$ .

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$\"\"$

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(a) $\"\"$ .

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(b) The probability to get less than $\"\"$ times is $\"\"$ .