Three distinct digits are selected from the set 1,2,3,4,5,6,7,8,9 and then the three digits are multiplied together to form a number N. The chance that N is a multiple of 10 is

Question

Three distinct digits are selected from the set 1,2,3,4,5,6,7,8,9 and then the three digits are multiplied together to form a number N. The chance that N is a multiple of 10 is (A) (2/7) (B) (2/21) (C) (7/21) (D) (11/42)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/4da104464d9c979d0fd14e2b65cd260d-.png" /> Let E: event that N is a multiple of 10 P ( E )= P (out of 3 digits, 5 is one of the digit and atleast one other is even) =( 4 C 2+ 4 C 1 ⋅ 4 C 1/ 9 C 3)=(6+16/84)=(22/84)=(11/42)

Q. Three distinct digits are selected from the set ${1, 2, 3, 4, 5, 6, 7, 8, 9}$ and then the three digits are multiplied together to form a number $N$ . The chance that $N$ is a multiple of 10 is

$\frac{2}{7}$

$\frac{2}{21}$

$\frac{7}{21}$

$\frac{11}{42}$

Let $E$ : event that $N$ is a multiple of 10
$P (E) = P$ (out of 3 digits, 5 is one of the digit and atleast one other is even)
$= \frac{^{4} C _{2} + ^{4} C _{1} \cdot ^{4} C _{1}}{^{9} C _{3}} = \frac{6 + 16}{84} = \frac{22}{84} = \frac{11}{42}$

Q. Three distinct digits are selected from the set {1,2,3,4,5,6,7,8,9} and then the three digits are multiplied together to form a number N. The chance that N is a multiple of 10 is

72​

212​

217​

4211​