How many six digit numbers can be formed using all the digits 1, 2, 3,

1.	How many six digit numbers can be formed using all the digits 1, 2, 3, 0, 7, 9?
Answer» Using all the digits 1, 2, 3, 0, 7, 9, six digit numbers are to be formed. ∴ Excluding digit 0, one of the five digits can be placed at the first place in ⁵P₁ ways Now, remaining 5 digits (including 0) can be arranged in remaining 5 places in ⁵P₅ ways. ∴ Total permutations for six digit numbers = ⁵P₁ × ⁵P₅ = 5 × 5! = 5 × 120 = 600 Hence, 600 numbers of 6 digit can be formed.

How many six digit numbers can be formed using all the digits 1, 2, 3, 0, 7, 9?

Answer»

Using all the digits 1, 2, 3, 0, 7, 9, six digit numbers are to be formed.
∴ Excluding digit 0, one of the five digits can be placed at the first place in ⁵P₁ ways

Now, remaining 5 digits (including 0) can be arranged in remaining 5 places in ⁵P₅ ways.

∴ Total permutations for six digit numbers

= ⁵P₁ × ⁵P₅

= 5 × 5!

= 5 × 120

= 600

Hence, 600 numbers of 6 digit can be formed.

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How many six digit numbers can be formed using all the digits 1, 2, 3, 0, 7, 9?

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