A four-digit natural number is formed using the digits from the set { 0 , 1 , 2 , 3 , 4 , 5 } , with repetition of digits allowed. Column I (Conditions) (A) The number formed is a multiple of 3. (B) T

Question

A four-digit natural number is formed using the digits from the set ${0, 1, 2, 3, 4, 5}$ , with repetition of digits allowed.

Column I (Conditions)

(A) The number formed is a multiple of 3.

(B) The number formed contains exactly two different digits.

(C) The number formed contains exactly three different digits.

(D) The number formed is odd.

Column II (Number of natural numbers)

(p) 480

(q) 540

(r) 360

(s) 175

TestHub · Accepted Answer

: For A → 5 × 6 × 6 × 2 = 360 For B → 5 C 2 ​ [ 2 ! 2 ! 4 ! ​ + 3 ! 4 ! ​ × 2 ] + 5 C 1 ​ [ 2 ! 3 ! ​ × 2 + 1 ] = 175 For C → 5 C 3 ​ × 2 ! 4 ! ​ + 5 C 2 ​ [ 9 × 2 + 6 ] = 360

Mathematics - Permutation & Combination Question with Solution | TestHub

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