Question

A student is allowed to choose 4 questions out of 7. In how many ways can he choose them?

35

30

25

40


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Answer 1

Answer:

35

Step-by-step explanation:

Formula to calculate combinations : nCr = n! / r!*(n-r)!

In this example n=7 , r=4 :

7C4 = 35

Answer 2

Given:

A student is allowed to choose 4 questions out of 7.

We have to find the total number of ways:

Solution:

The total number of ways = $^7C_4$

We know that,

$^nC_r$ = $\dfrac{n!}{(n-r)!.r!}$

Here, n = 7 and r = 4

$^7C_4$ = $\dfrac{7!}{(7-4)!.4!}$

$=\dfrac{4!(5\times 6\times 7)}{(3)!.4!}$

$=\dfrac{5\times 6\times 7}{1\times 2\times 3}$

$=\dfrac{5\times 6\times 7}{1\times 2\times 3}$

= 5 × 7

= 35

∴ The total number of ways = 35

Thus, the required "option a) 35" is correct.