A bag contains $7$ balls of same color. What is the correct expression to find the number of ways for selecting $5$ balls?

^{7} P_{5}

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^{7} C_{2}

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^{7} C_{3}

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^{7} P_{2}

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Solution

The correct option is B $^{7} C_{2}$
Given that: Total number of balls $= 7$
Here, order of selection does not matter
So, $5$ balls can be selected as $^{7} C_{5}$ ways

Note: $^{n} C_{r} =^{n} C_{(n - r)}$
So,
$^{7} C_{5} =^{7} C_{(7 - 5)} =^{7} C_{2}$

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A bag contains 7 balls of same color. What is the correct expression to find the number of ways for selecting 5 balls?

The correct option is B 7C2Given that: Total number of balls =7 Here, order of selection does not matter So, 5 balls can be selected as 7C5 ways Note: nCr=nC(n−r) So, 7C5=7C(7−5)=7C2

A bag contains $7$ balls of same color. What is the correct expression to find the number of ways for selecting $5$ balls?

The correct option is B $^{7} C_{2}$
Given that: Total number of balls $= 7$
Here, order of selection does not matter
So, $5$ balls can be selected as $^{7} C_{5}$ ways

Note: $^{n} C_{r} =^{n} C_{(n - r)}$
So,
$^{7} C_{5} =^{7} C_{(7 - 5)} =^{7} C_{2}$