Question

a set P has 20 elements .The number of subsets of P containing odd number of elements is ?

Answer 1

20C1 +20C3+20C5+...20C19 = 2^(20-1) = 2^19 = 524288 subsets

Answer 2

Answer:

Hence, the number of subsets of P containing odd number of elements is:

524288

Step-by-step explanation:

a set P has 20 elements .

The number of subsets of P containing odd number of elements is given by the help of the combination formula as:

The odd number of elements are given by:

1,3,5,7,9,11,13,15,17,19.

Hence, the number of subsets are:

$20_C_1+20_C_3+20_C_5+20_C_7+20_C_9+20_C_{11}+20_C_{13}+20_C_{15}+20_C_{17}+20_C_{19}$

We know that the formula of combination is given as:

$n_C_r=\dfrac{n1}{r!(n-r)!}$

Hence, on calculating the above value we have:

$20_C_1+20_C_3+20_C_5+20_C_7+20_C_9+20_C_{11}+20_C_{13}+20_C_{15}+20_C_{17}+20_C_{19}=524288$

Hence, the number of subsets of P containing odd number of elements is:

524288