Question

find the number of numbers of 6 digit without repetition formed with the digit 123456 in which 5 always occurs in tenth place​

Answer 1

Here, repetition is not allowed.

Here the tens place contain a constant value, i.e., 5, so we may only consider the remaining 5 places.

Well,

→ lakhs place can only occupy one among the digits 1, 2, 3, 4 and 6, i.e., 5 outcomes

→ once lakhs place is occupied, ten thousands place can occupy 4 digits

→ after, thousands place can only occupy 3 digits

→ then, hundreds place can only occupy 2 digits

→ tens place can only occupy the digit 5, i.e., only 1 outcome

→ finally, ones place can only occupy only 1 digit

Hence, total no. of permutations = 5 × 4 × 3 × 2 × 1 × 1 = 120