Solve the following
Question:

5C1 + 5C2 5C3 + 5C4 +5C5 is equal to

(a) 30

(b) 31

(c) 32

(d) 33

Solution:

(b) 31

${ }^{5} C_{1}+{ }^{5} C_{2}+{ }^{5} C_{3}+{ }^{5} C_{4}+{ }^{5} C_{5}$

 

= ${ }^{5} C_{1}+{ }^{5} C_{2}+{ }^{5} C_{2}+{ }^{5} C_{1}+{ }^{5} C_{5}$

$=2 \times{ }^{5} C_{1}+2 \times{ }^{5} C_{2}+{ }^{5} C_{5}$

 

$=2 \times 5+2 \times \frac{5 !}{2 ! 3 !}+1$

$=10+20+1$

 

$=31$

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