3 persons have 4 coats, 5 waist coats and 6 hats. The number of ways in which they put on the clothes are:

Question

3 persons have 4 coats, 5 waist coats and 6 hats. The number of ways in which they put on the clothes are: (A)  43× 53× 63  (B)  4× 5× 6  (C)  4 ! 5 ! 6 !  (D) none of these

Tardigrade Admin · Accepted Answer

Total, number of coats =4, waist coats =5=5 and hats =6 The total number of ways, in which one person put the clothes =4 × 5 × 6 The total number of ways, that all three persons put the clothes =43 × 53 × 63

Q. $3$ persons have $4$ coats, $5$ waist coats and $6$ hats. The number of ways in which they put on the clothes are:

$4^{3} \times 5^{3} \times 6^{3}$

$4 \times 5 \times 6$

$4! 5! 6!$

none of these

Total, number of coats $= 4$ , waist coats $= 5 = 5$ and hats $= 6$
The total number of ways, in which one person put the clothes $= 4 \times 5 \times 6$
The total number of ways, that all three persons put the clothes $= 4^{3} \times 5^{3} \times 6^{3}$

Q. 3 persons have 4 coats, 5 waist coats and 6 hats. The number of ways in which they put on the clothes are:

43×53×63

4×5×6

4!5!6!