Question 2 and 3, Review Exercise 6

Solutions of Question 2 and 3 of Review Exercise 6 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

How many words can be formed by using four distinct alphabets?

Solution.

Number of word we can make using $4$ different alphabets out of $26$ alphabets is
$$^{26}P_4=358800$$

How many $3$-digit numbers are there which have $0$ at unit place?

Solution.

In $3$ digit numbers unit, tens and $100's$ place may be filled in 10 ways using digits #0# to $9$.
So total possible $3$ digit numbers are $$=10\times 10\times10=1000$$
If we fix units place at $0$ remaining two places may be filled in $10$ ways,
so total possible $3-$digit numbers having $0$ at units place are $$=10\times 10=100$$

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