Discussion

Explanation:

Case 1: Number of 4-digit numbers
__ __ __ __
Here, 
unit’s digit can be either 2, 3, 4 or 5 i.e., 4 ways,
ten’s digit can be chosen from remaining 5 numbers in 5 ways,
hundred’s digit can be chosen from remaining 4 numbers in 4 ways.
thousand’s digit can be chosen from remaining 3 numbers in 3 ways.
⇒ Total such 4-digit numbers = 4 × 5 × 4 × 3 = 240

Case 2: Number of 5-digit numbers
__ __ __ __ __
Here, 
unit’s digit can be either 1, 2, 3, 4 or 5 i.e., 5 ways,
ten’s digit can be chosen from remaining 5 numbers in 5 ways,
hundred’s digit can be chosen from remaining 4 numbers in 4 ways.
thousand’s digit can be chosen from remaining 3 numbers in 3 ways.
ten thousand’s digit can be chosen from remaining 2 numbers in 2 ways.
⇒ Total such 5-digit numbers = 5 × 5 × 4 × 3 × 2 = 600

Case 2: Number of 6-digit numbers
__ __ __ __ __
Here, 
unit’s digit can be either 1, 2, 3, 4 or 5 i.e., 5 ways,
ten’s digit can be chosen from remaining 5 numbers in 5 ways,
hundred’s digit can be chosen from remaining 4 numbers in 4 ways.
thousand’s digit can be chosen from remaining 3 numbers in 3 ways.
ten thousand’s digit can be chosen from remaining 1 number in 1 way.
One lakh’s digit
⇒ Total such 6-digit numbers = 5 × 5 × 4 × 3 × 2 × 1 = 600

∴ Total required numbers = 240 + 600 + 600 = 1440.

Hence, option (c).

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