In an admission test, there are 15 multiple choice questions. Each question is followed by 4 alternatives to choose. Out of these there may be one or more than one correct answers. If a student attempts all the 15 questions and marks the answers randomly, then number of different ways he can answer the question paper is

Question

In an admission test, there are 15 multiple choice questions. Each question is followed by 4 alternatives to choose. Out of these there may be one or more than one correct answers. If a student attempts all the 15 questions and marks the answers randomly, then number of different ways he can answer the question paper is (A)  4 × 15 C 4 (B) 1515 (C) 415 (D) 4 ! ⋅ 15 !

Tardigrade Admin · Accepted Answer

These are 15 multiple type questions. Students attempts all 15 questions. The number of way student can answer the questions is =mn m =15 n =15 ⇒ (15)15

$^{4 \times 15} C_{4}$

$1 5^{15}$

$4^{15}$

$4! \cdot 15!$

These are 15 multiple type questions. Students attempts all 15 questions.
The number of way student can answer the questions is $= m^{n}$
$m = 15$
$n = 15$
$\Rightarrow (15)^{15}$

4×15C4​

1515

415

4!⋅15!

These are 15 multiple type questions. Students attempts all 15 questions. The number of way student can answer the questions is =mn m=15 n=15 ⇒(15)15

$^{4 \times 15} C_{4}$

$1 5^{15}$

$4^{15}$

$4! \cdot 15!$

These are 15 multiple type questions. Students attempts all 15 questions.
The number of way student can answer the questions is $= m^{n}$
$m = 15$
$n = 15$
$\Rightarrow (15)^{15}$