5 C1-5 C2-5 C3-5 C4-5 C5 is equal toa 30b 31c 32d 33

(b) 31 nbsp; nbsp; nbsp; nbsp; 5C1 #160;+ #160;5C2 #160;+ #160;5C3 #160;+ #160;5C4 #160;+ #160;5C5 nbsp;= #160;5C1 #160;+ # ...

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Byju's Answer

Standard VII

Mathematics

Subtraction of Algebraic Expressions

5 C1+5 C2+5 C...

Question

⁵C₁ + ⁵C₂+ ⁵C₃ + ⁵C₄ +⁵C₅ is equal to
(a) 30
(b) 31
(c) 32
(d) 33

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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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5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to (a) 30 (b) 31 (c) 32 (d) 33

(b) 31 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 5C1 + 5C2 + 5C2 + 5C1 + 5C5 = 2 × 5C1 + 2 × 5C2 + 5C5= 2 × 5 + 2 × 5!2! 3! + 1 = 10 + 20 + 1 = 31

⁵C₁ + ⁵C₂+ ⁵C₃ + ⁵C₄ +⁵C₅ is equal to
(a) 30
(b) 31
(c) 32
(d) 33

(b) 31

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

$= 2 \times^{5} C_{1} + 2 \times^{5} C_{2} +^{5} C_{5} = 2 \times 5 + 2 \times \frac{5!}{2! 3!} + 1 = 10 + 20 + 1 = 31$