Question

The number of ways of selecting a prime number from first 10 natural numbers is
${\text{A}}{\text{. }}{}^{10}{C_4}$
${\text{B}}{\text{. }}{}^4{C_{10}}$
${\text{C}}{\text{. }}{}^{10}{P_4}$
${\text{D}}{\text{. }}{}^{10}{C_5}$

Answer 1

Hint: The prime numbers in the range 1 to 10 are 2, 3, 5, 7. So, use the formula ${}^n{C_r}$, where n is the total numbers and r is the total numbers to be selected from the given range.

Complete step-by-step answer:
Now, we know that the prime numbers in the range 1 to 10 are 2, 3, 5, 7.
Therefore, total number of prime numbers = 4.
And the total numbers from 1 to 10 = 10.
Therefore, No. of ways of selecting is given as ${}^n{C_r}$.
Putting the value of n = 10 and r = 4, we get-
$N = {}^n{C_r} = {}^{10}{C_4}$.
Hence, the correct option is ${\text{A}}{\text{. }}{}^{10}{C_4}$.

Note: Whenever such types of questions appear, then write the first 10 numbers and then write the numbers which are prime among them. Then, use the standard formula of selecting r numbers from n numbers, i.e., ${}^n{C_r}$, put the value of n = 10 and r = 4 to find the answer.