Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

The nine cards carry the numbers 1, 2, 2, 3, 3, 4, 6, 6, 6.
(i(a))[4]

All nine cards are laid out in a row, forming a 9-digit number. Determine how many different 9-digit numbers can be formed in this way if all the even digits are adjacent.

(i(b))[3]

All nine cards are arranged in a line, producing a 9-digit number. Determine how many different 9-digit numbers can be formed in this way if the first and last digits are both odd.

(ii(a))[2]

Three of the nine cards are selected and arranged in a line to form a 3-digit number. Determine how many different numbers can be formed in this way if no digit is repeated.

(ii(b))[2]

Three of the nine cards are selected and arranged in a line to form a 3-digit number. Determine how many different numbers can be formed in this way if the number is between 200 and 300.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: A suitable single-term numerator such as $6!$ or $(x)4!$

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