5 C 1-5 C 2-5 C 3-5 C 4-5 C 5 is equal toA- 31B- 30C- 32D- 33

The correct option is A 31 ^5C_1 + ^5C_2 + ^5C_3 + ^5C_4 + ^5C_5 = ^5C_1 + ^5C_2 + ^5C_2 + ^5C_1 + ^5C_5 = 2 ×^5C_1 + 2 ×^5C_2 + ^5C_5 = 2 × 5 + 2 ×5!/2! 3! ...

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Byju's Answer

Standard XII

Mathematics

nCr Definitions and Properties

5 C 1+5 C 2+5...

Question

$^{5} C_{1} +^{5} C_{2} +^{5} C_{3} +^{5} C_{4} +^{5} C_{5}$ is equal to

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Solution

The correct option is 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

The correct option is 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

$^{5} C_{1} +^{5} C_{2} +^{5} C_{3} +^{5} C_{4} +^{5} C_{5}$ is equal to

The correct option is B
31

$^{5} C_{1} +^{5} C_{2} +^{5} C_{3} +^{5} C_{4} +^{5} C_{5} =^{5} C_{1} +^{5} C_{2} +^{5} C_{2} +^{5} C_{1} +^{5} C_{5} = 2 \times^{5} C_{1} + 2 \times^{5} C_{2} +^{5} C_{5} = 2 \times 5 + 2 \times \frac{5!}{2! 3!} + 1 = 10 + 20 + 1 = 31$