Question

in how many ways can we choose a number from 1, 2, 3, 4, 5, 6 which is either a perfect square or a multiple of 3.

Answer 1

Answer:

in how many ways can we choose a number from 1, 2, 3, 4, 5, 6 which is either a perfect square or a multiple of 3.

Step-by-step explanation:

6

Answer 2

Given:

Total sample space$={1,2,3,4,5,6}$

To find: the number of ways to choose a number from the given sample space such that it is either a perfect square or a multiple of 3.

Solution:

Know that from the question, the total number of numbers in the sample space are 6. and the numbers in the sample space that are either a perfect square or a multiple of 3 are $3,4,6$.

Therefore,

the number of ways a number is chosen from $1,2,3,4,5,6$ is,

$\[\begin{array}{l}{ = ^6}{C_1}\\ = \frac{{6!}}{{\left( {6 - 1} \right)!1!}}\end{array}\]$

$\[ = \frac{{6!}}{{5!}}\]$

$\[\begin{array}{l} = \frac{{6 \times 5!}}{{5!}}\\ = 6\end{array}\]$ways.