5 -digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000 , then p: q is

Question

5 -digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000 , then p: q is (A) 6: 5 (B) 3: 2 (C) 5: 3 (D) 4: 3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/c0b89f223191825a11de79592c178458-.png" /> p =5 × 4 × 3 × 2 × 1 =5 !=120 q =3 × 4 × 3 × 2 × 1 =3 ⋅ 4 !=72 ∴ ( p / q )=(120/72)=(5/3)=5: 3

Q. $5$ -digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ be the number of such numbers that exceed $20000$ and $q$ be the number of those that lie between $30000$ and $90000$ , then $p : q$ is

$6 : 5$

$3 : 2$

$5 : 3$

$4 : 3$

$p = 5 \times 4 \times 3 \times 2 \times 1$
$= 5! = 120$
$q = 3 \times 4 \times 3 \times 2 \times 1$
$= 3 \cdot 4! = 72$
$∴ \frac{p}{q} = \frac{120}{72} = \frac{5}{3} = 5 : 3$

Q. 5 -digit numbers are to be formed using 2,3,5,7,9 without repeating the digits. If p be the number of such numbers that exceed 20000 and q be the number of those that lie between 30000 and 90000 , then p:q is

6:5

3:2

5:3

4:3